# Trigonometry

How do you verify the equation is an identity?
Tan^2x-tan^2y=sec^2x-sec^2y

and, how do you factor and simplify,
cscx(sin^2x+cos^2xtanx)/sinx+cosx

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. One of the basic identities is
tan^2 A + 1 = sec^2 A which gives Tan^2 A = sec^2 A - 1

so
Left side
= tan^2x-tan^2y
= sec^2x - 1 -(sec^2y - 1)
= sec^2x - sec^2y
= Right Side

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. For the second, I will assume you meant

cscx(sin^2x+cos^2xtanx)/(sinx+cosx)
= 1/sinx(sin^2x + cos^2xsinx/cosx)/(sinx + cosx)
= 1/sinx(sin^2x + sinxcosx)/(sinx+cosx)
= (sinx + cosx)/sinx + cosx)
= 1

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### math;)

Julia wants to simplify the term sec^2 theta-1/cot^2 theta+1 in a trigonometric identity that she is proving. Which of the following identities should use to help her? Select all that apply. (2 ANSWERS) a. sin^2 theta+cos^2

2. ### Math

What is a simplified form of the expression [sec^2x-1]/[(sinx)(secx)]? a. cot x b. csc x c. tan x***** d. sec x tan x I think this is the correct answer, but I do not understand why. Can someone please explain?

3. ### math

Prove the trigonometric identity. tan x+cot x/csc x cos x=sec^2 x __= sec^2x __= sec^2x __ = sec^2x __= sec^2x __ = sec^2x 1/cos^2x=sec^2x sec^2x=sec^2x

4. ### Math

What is a simplified form of the expression sec^2x-1/sin x sec x ? a)cot x b)csc x c)tan x d)sec x tan x Please help me :(

1. ### physics (speed of plane by radar)

The radar stations A and B, separated by the distance a = 500 m, track the plane C by recording the angles α and β at 1-second intervals, If three successive readings are shown in the table,calculate the speed v of the plane and

2. ### Trigonometry

Find the exact value of tan(a-b) sin a = 4/5, -3pi/2

3. ### math

Prove that the equation Is an identity. Sec^4x - Tan^4x = Sec^2x + Tan^2x

4. ### Calc

If f(x)= sec x, find f"(Pi/4) I am not sure how to take the 2nd derivative? f'(x)= sec x tan x f"(x)=??? Is it f"(x)= (sec x tan x)(sec^2x)??? Please Help!

1. ### Mathematics

(cos 2x)/(1/(cos x)) * (sin(pi + x))/(tan x) = (sec(x) - csc(x)) * (csc(x))/(sec^2 x) * (1 - cos^2 x) My friend and I are having a debate on the true identity of this equation, however my friend learned this subject and I did not.

2. ### Trigonometry

Simplify each expression using the fundamental identities. 1. Sec x csc x / sec^2x+csc^2x 2. Sec x + tan x / sec x + tan x - cos x

3. ### Trig

Find secx if sinx = -4/5 and 270 < x < 360. tan^2x+1=sec^2x (-4/5)^2+1=sec^2x 16/25+1=sec^2x 17/25=sec^2x sqrt 17/5 I don't know if it should be positive or negative.

4. ### Calculus PLEASE check my work ,

1.) which of the following represents dy/dx when y=e^-2x Sec(3x)? A.3e^-2x sec(3x) tan (3x)-2e^-2x Sec(3x)