Prove that sin(x) + tan(x) = 1 + sec(x)/csc(x) by using trigonometric identities.

Answers

Answer 1

Answer:

Step-by-step explanation:

sin(x) + tan(x) =sin(X) + sin(x)/cos(x)

=sinx(1+1/cosx)

=Sinx(1+secx)

=1+secx/cosecx. (Since sinx=1/cosecx)

Hence LHS=RHS proved


Related Questions

Points (−6, 3) and (−6, −3) on the coordinate grid below show the positions of two dogs at a park:






Which statement best describes the relationship between the positions of the two players?

Dog 1's position is Dog 2's position reflected across the y-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.
Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.
Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the x-coordinates of Dog 1 and Dog 2 are different.
Dog 1's position is Dog 2's position reflected across the y-axis; only the signs of the x-coordinates of Dog 1 and Dog 2 are different.

Answers

Answer:

The answer is B.

Step-by-step explanation:

Points (−6, 3) and (−6, −3) on the coordinate grid below show the positions of two dogs at a park:

A coordinate plane is shown. There is a point at negative 6, 3 labeled Dog 1. There is a point at negative 6, negative 3 labeled Dog 2.

Solve for x. Round answer to the nearest tenth, if necessary

Answers

Answer:

x=15

Step-by-step explanation:

9²+12²=c²

81+144=c²

225=c²

√225=√c

15=c

The measure of the x is 15.

Given

The length of the base is 9 and the perpendicular is 12.

What is the Pythagoras theorem?

Pythagoras theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

The length of the hypotenuse is x.

Therefore,

[tex]\rm (Hypotenuse )^2= (Base)^2+ (Perpendicular)^2\\\\(x)^2=(9)^2+(12)^2\\\\144+81=x^2\\\\x^2 = 144+81\\\\x^2=225\\\\x=15[/tex]

Hence, the measure of the x is 15.

To know more about Pythagoras theorem click the link given below.

https://brainly.com/question/343682

Translate the sentence six less than the product of four and a number is -2 into an equation

Answers

Answer:

4x - 6 = -2

Step-by-step explanation:

i dont really know how to explain this one

Answer:

[tex]4x-6=-2[/tex]

Step-by-step explanation:

So since it says 6 is less than that means we will be putting the 6 in front of the number that's going to be 4x because the product of 4 and x is shown by 4x. Then lastly it says all "is -2" that means all that equals -2.

3 lines are shown. A line with points C, A, F intersects a line with points E, A, B at point A. A line extends from point A to point D in between angle E A F. Angle C A E is 61 degrees, angle D A F is 90 degrees, and angle F A B is 61 degrees. Find the following angle measures. mAngleEAD = ° mAngleCAB = °

Answers

Answer:

m < EAD = 29 degrees

m < CAB = 119 degrees

Given :

The question states that m < CAE = m<FAB = 61 degrees and m<DAF = 90 degrees

Solution:

1. Since line CAF and EAB intersect each other, m<CAF = m< EAF - (opposite vertical angles are equivalent)

2. m<BAC + m<EAC = 180 degrees (sum of linear pair)

3. m<CAB = 180 degrees - m<EAC

4. Equation 1: m<CAB = m<EAF = 119 degrees

5. m<EAF = m<EAD + m< DAF

6. m<EAD = m<EAF - m<DAF

7. m<EAD = 119 degrees-90 degrees = 29 degrees

Hope this helps!!! :)

Attached photo work is created by another brainly user named tallinn.

Click on this link to find his work and possibly more information of the answer. Thanks!

m < EAD = 29 degrees

m < CAB = 119 degrees

It is given that Angle C A E is 61 degrees,

angle D A F is 90 degrees,

angle F A B is 61 degrees

We need to find mAngleEAD and  mAngleCAB

What is sum of linear pair angles?

The sum of linear pairs is 180 degrees

Since line CAF and EAB intersect each other, m<CAF = m< EAF - (opposite vertical angles are equivalent)

m<BAC + m<EAC = 180 degrees (sum of linear pair)

m<CAB = 180 degrees - m<EAC

Equation 1: m<CAB = m<EAF = 119 degrees

m<EAF = m<EAD + m< DAF

m<EAD = m<EAF - m<DAF

m<EAD = 119 degrees-90 degrees = 29 degrees

To learn more on sum of linear angles visit: https://brainly.com/question/620263

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can someone please help me with this :( asap

Answers

b

こんにちは

mmmmmmmmnnnnnnnnnnnnnnnnnnnnnnn

PLEASE HELP!!! THANK YOU!!!

Answers

Answer:

1st attachment :-

counters left = 160

fraction of counters left = 160/400

=2/5

2nd attachment :-

a) how much cheaper = 13 ×(35.43 -15.37)

= 260.78

b) B.underestimate

Answer:

260.78

Step-by-step explanation:

what is positive 1 plus negative 6

Answers

Answer:

-5

Step-by-step explanation:

When answering these problems, I like to think of dirt stacks. (Weird, but it helps.)

Okay, so you have a stack of dirt one foot off the ground. Then you dig six feet down, including the stack.  Because the stack will be 5 feet into the ground now, the answer is -5.

Helllp it's due tonight ​

Answers

it’s linear, the rate is -2/2.5 The rate is staying constant so therefore it’s linear and not exponential.

I attached a file pls answer quick i gotta sleep

Answers

Answer:

P(2, 3.5)

Step-by-step explanation:

If P partitions AB in the ratio 1:1, then P is the midpoint of AB

Using midpoint formula to find its coordinates

A = (1, 2), B = (3, 5) as per graph

Finding P:

P = ((1+3)/2, (2+5)/2) = (2, 3.5)

It took everly 55 minutes to run a 10-kilometer race last weekend. If you know that 1 kilometer equals 0.621 mile, how many mintues did it take everly to run 1 mile during the race?

Answers

Answer:

8.9 minutes

Step-by-step explanation:

Converting Everly Kilometer race to miles

1 km = 0.621 miles

10 km =

10 × 0.621 miles

= 6.21 miles

Hence,

6.21 miles = 55 minutes

1 mile = x minutes

Cross Multiply

6.21 × x = 55 × 1

x = 55 minutes/6.21

x = 8.8566827697 minutes

Approximately = 8.9 minutes

(please help asap, thank you!)
When one side of the Earth is at high tide, then the opposite side of the Earth is also at high tide?

True or False?

Answers

Step-by-step explanation:

When one side of the Earth is at high tide, then the opposite side of the Earth is also at high tide?

(True)

what is 15/8 simplyfied ?

Answers

Answer:

mixed number 1 7/8 or decimal form 1.875

Answer:

it cant be simplified but it can be converted into a mixed number. which is

1 7/8. hope this helps <3

Step-by-step explanation:

You are looking for a new cell phone plan. The first company, Cellular-Tastic (f), charges a monthly fee of $35 and $0.11 per minute of use. Dirt-Cheap Cell (g) charges a monthly fee of $55 and $0.01 per minute of use.
a. How many minutes would you need to use for the cell phones to cost the same amount?
b. Create a graph to model this situation and describe the graph in writing in the space provided. Include the general shape and any intersections or intercepts.
c. Using your graph, explain when each company would be a better option.

Answers

Answer:

A. 200 minutes

Step-by-step explanation:

What is the simplified form of the expression V-64?

Answers

Answer:

v32

Step-by-step explanation:

i think not sure tho

What is the slope of y=-x+7y?

Answers

Answer:

The slope of y=-x+7y is m = - 1.

Step-by-step explanation:

y = m x + c

The intercept is (0,7) | constant term.

The slope is m=1/6.

Two friends tried to rewrite the expression 12 + 20 using the distributive property. Which friend is correct? Explain.

Ahmad: 6(3+7)

Deena: 4(3+5)

Answers

Answer:

Deena

Step-by-step explanation:

Solve each proportion.

5/2=6/x

Wat is x

Answers

Answer:

12/5

Step-by-step explanation:

5/2 = 6/x

in order to solve for x, you can do cross multiplication hence,

5x = 6(2)

x = 12/5

Answer:

12/5

Step-by-step explanation:

5/2=6/x

5x=12

X=12/5.

So the answer is 12/5

Felicia ran a 4-mile race in 28 minutes. Complete the table to represent Felicia’s average rate of speed during the race.

Answers

Answer:

she runs an average 1mile every 7 minutes

Step-by-step explanation:

sorry if this does not help if this is not what u r looking for maybe clarify

hope this helps also i don't see where the chart is for the question

A slide 15 feet long makes an angle of 330 with its vertical ladder. To the
nearest foot, how tall is the slide?

Answers

Answer:

13ft

Step-by-step explanation:

Kindly find attached a rough draft of the situation.

Step one:

Given data

The length of the slide represents the

Hypotenuse of the situation on the rough sketch

Angle =33°

Required

The height of the ladder which is the adjacent of the rough sketch represented by x

Step two:

Applying SOH CAH TOA

Cos θ= adj/hyp

Cos 33=x/15

0.84=x/15

Cross multiplying

x=0.84*15

x=12.6

To the nearest foot the ladder is 13ft tall

16x what equals -112

Answers

Answer:

-7

Step-by-step explanation:

16x=-112

x=-112/16

x=-7

PLS GIVE BRAINLIEST

if an item sells for $44.28 per kilograms, how many cents per ounce does the item cost? Round the answer to the nearest ten-thousandth place ​

Answers

Answer:

The item cost 125.53159 cents per ounce if its sales price is $44.28 per kilograms

Step-by-step explanation:

The sale price of item is $44.28 per kilograms. We need it to convert into cents per ounce.

We know that 1 dollar per kilogram = 2.83495 cents per ounce

So, 44.28 dollars per kilograms = 2.83495 * 44.28 cents per ounce

                                                     = 125.53159 cents per ounce

So, the item cost 125.53159 cents per ounce if its sales price is $44.28 per kilograms

A store is advertising a 25% off sale. Mikale purchases a swimming pool for $225. What was the original price of the pool?
A.
$450.75
B.
$300.00
C.
$655.50
D.
$281.25

Answers

Answer:

B

Step-by-step explanation:

which of the following is the equation logx4=-2 written in exponential form

Answers

X^-2=4. You got it correct:)

1. The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;

⇒ x⁻² = 4

2. The value of √e⁷/e⁵ will be;

⇒ e

3. The equivalent expression of 3 will be;

⇒ ln e³

What is an expression?

Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

1. The expression is the equation [tex]log_{x} 4 = - 2[/tex].

2. The equation is √e⁷/e⁵.

3. The number is 3.

Now,

The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] is calculated as;

[tex]log_{x} 4 = - 2[/tex]

By the definition of logarithmic, we get;

4 = x⁻²

Hence, The exponential form of the equation [tex]log_{x} 4 = - 2[/tex] will be;

⇒ x⁻² = 4

2. The equation is √e⁷/e⁵.

Solve as;

√e⁷/e⁵ = √ e ⁷ ⁻ ⁵

           = √ e²

           = e

Thus,  The value of √e⁷/e⁵ will be;

⇒ e

3. Since, by the definition of logarithmic;

[tex]ln_{e} e = 1[/tex]

So, By option 1;

[tex]ln_{e} e^3[/tex] = [tex]1 * 3[/tex] = [tex]3[/tex]

Thus, The equivalent expression of 3 will be;

⇒ ln e³

Learn more about the expression visit:

https://brainly.com/question/1859113

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At the first track meet, Bobby threw the shot put feet. At the second track meet he threw the shot put feet.
Which of the following expressions could be used to find the distance he improved his throw from the first track meet to the second track meet?
A. 423/4 + 44 1/2
B. 42 3/4 - ( -44 1/2 )
C. 44 1/2 - ( 42 3/4 )
D. 42 3/4 - 44 1/2

Answers

Answer: it has to be D

Answer:

The Answer is D) Just did the test!!

Step-by-step explanation:

can you help me with this I need it done by tomorrow thank you

Answers

Answer:

x = 17deg

Step-by-step explanation:

angle DCE = angle ACB (vertically opposite angles)

therefore,

x + 100 = 4x + 49

3x = 51

x = 17deg

Answer:

X=

Step-by-step explanation:

First you have to divide the shape into to triangles. Triangle CED and triangle ACB.

Second you have to find what angle C is in the triangle ACB. For this you'll have to:

Find out which of the sides are which. For triangle ACB, side CB is the hypotenuse, CA and AB are adjacent.

The formula we use is [tex]a^{2} +b^{2} =c^{2}[/tex].  a and b are adjacent and c is hypotenuse.

When you found what angle C is, you can go on and to the second triangle same theorem applies to the second triangle [tex]a^{2} +b^{2} =c^{2}[/tex]. At this stage you will already know two angles, 100 and c, so finding E using this formula will be easy

Dos padres de familia deseaban saber cuáles son los costos de los uniformes escolares que compraron a sus hijos, ya que el primero padre de familia realizó la siguiente compra: 2 pantalones y 2 playeras pagando por ello $820, el segundo padre de familia realizó la siguiente compra, 1 pantalón y 3 playeras pagando por ello $490. Resuelve los siguente cuestionamientos ¿Los padre de familia pagaron al mismo precio cada pantalón y playera? ¿Existe diferencia entre x e y en la ecuación 1 y con respecto a la ecuación 2?

Answers

Answer:

a) ¿Pagaron los padres el mismo precio por cada pantalón y camisa?

Sí, los padres pagaron la misma cantidad por cada pantalón y camisa porque,

1 camisa = $ 40

1 pantalón = $ 370

b) ¿Hay alguna diferencia entre xey en la ecuación 1 y con respecto a la ecuación 2?

Sí, hay una diferencia

Step-by-step explanation:

Dos padres querían saber el costo de los uniformes escolares que compraban para sus hijos, ya que

Representemos pantalones = p

camisas = s

Derivamos las 2 ecuaciones

El primer padre hizo la siguiente compra: 2 pantalones y 2 camisas pagando $ 820 por ella

2p + 2s = 820 ........ Ecuación 1

El segundo padre hizo la siguiente compra, 1 pantalón y 3 camisas pagando $ 490.

p + 3s = 490 ....... Ecuación 2

p = 490 - 3 s

Resolvamos el precio de cada pantalón y camisa.

Nosotros sustituimos

2p + 2s = 820

2 (490 - 3 s) + 2 s = 820

980 - 6s + 2s = 820

980 - 820 = 6 segundos - 2 segundos

160 = 4 s

s = 160/4

s = $ 40

Por lo tanto, el costo de cada camisa = $ 40

El costo de los pantalones =

p = 490 - 3 s

p = 490 - 3 (40)

p = 490 - 120

p = $ 370

El costo de cada pantalón = $ 370

Resuelve las siguientes preguntas.

a) ¿Pagaron los padres el mismo precio por cada pantalón y camisa?

Sí, los padres pagaron la misma cantidad por cada pantalón y camisa porque,

1 camisa = $ 40

1 pantalón = $ 370

b) ¿Hay alguna diferencia entre xey en la ecuación 1 y con respecto a la ecuación 2?

Sí, hay una diferencia

Planteando y resolviendo un sistema de ecuaciones, veremos que cada playera cuesta $40 y cada pantalon cuesta $370.

Definamos:

x = precio de pantalonesy = precio de playeras.

Por la información dada, tenemos que:

2*x + 2*y = $820

1*x + 3*y = $490

Primero respondamos las preguntas:

Notar que ambas preguntas basicamente preguntan la misma cosa:

¿Existe diferencia entre x e y en la ecuación 1 y con respecto a la ecuación 2?

Es realmente imposible saber la respuesta, pero debemos asumir que no, dado que si x e y representan diferentes cosas en cada ecuación, entonces las variables no estan definidas, y el problema es imposible de resolver.

Así que asumimos que los precios son los mismos.

con esto en mente, podemos resolver el sistema:

2*x + 2*y = $820

1*x + 3*y = $490

Primero, aislamos una variable en una ecuación, en este caso voy a aislar x en la segunda:

x = $490 - 3*y

Reemplazamos eso en la primera:

2*($490 - 3*y) + 2*y = $820

$980 - 4*y = $820

$980 - $820 = 4*y

$160/4 = y  = $40

Es decir, el precio de cada playera es $40.

Mientras que:

x = $490 - 3*$40 = $370

Cada pantalon cuesta $370

Si quieres aprender más, puedes leer:

https://brainly.com/question/17174746

Please Help ASAP!! Marking Brainliest!! Divide [tex]12x^2 + 4x^3 + 18 + 16x[/tex] by [tex]2x + 4[/tex].

a.) [tex]2x^2 + 2x + 3 + \frac{5}{x + 4}[/tex]
b.) [tex]2x^2 + 2x + 4 - \frac{2}{x + 4}[/tex]
c.) [tex]2x^2 + 2x + 4 + \frac{2}{2x + 4}[/tex]
d.) [tex]2x^2 + 2x + 3 + \frac{14}{x + 4}[/tex]

Answers

Answer:

The answer is C

Step-by-step explanation:

Just calculate it

help plzzzzzzz i really need it

Answers

Answer:

2n+2*3-6n

(-2*-3)+4n-(4n*2)

can you please help meee ,due at 11!

Answers

Answer:

x-intercept: -1/2

y-intercept: 5/2

Step-by-step explanation:

How many solutions does the equation −4y + 4y + 2 = 2 have?
a. Two
b. None
c. One
d. Infinitely many

Answers

Answer:

D

Step-by-step explanation:

Let's solve your equation step-by-step.

−4y+4y+2=2

Step 1: Simplify both sides of the equation.

−4y+4y+2=2

(−4y+4y)+(2)=2(Combine Like Terms)

2=2

2=2

Step 2: Subtract 2 from both sides.

2−2=2−2

0=0

Answer:

All real numbers are solutions.

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