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## Homework Statement

All that has to be done is proving that these two sides are equal. Basically, you just work through the problem until both sides are the same.

(csc(x)-sec(x))/(csc(x)+sec(x)) = (tan(x)-1)/(tan(x)+1)

## Homework Equations

sin

^{2}x + cos

^{2}x = 1

csc(x) = 1/sin(x)

sec(x) = 1/cos(x)

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

sin(-x) = -sin(x)

cos(-x) = -sin(x)

## The Attempt at a Solution

coverted to terms of sin and cos

(1/sinx-1/cosx)/(1/sinx+1/cosx) = ((sinx/cosx)-1)/((sinx/cosx)+1)

flipped and multiplied, then started simplifying

sinx/sinx - sinx/sinx + cosx/sinx - sinx/cosx = sinxcosx/sinxcosx + sinx/cosx - cosx/sinx - 1

continued simplifying

cosx/sinx - sinx/cosx = 1 - 1 + sinx/cosx -cosx/sinx

cosx/sinx - sinx/cosx = sinx/cosx - cosx/sinx

This is where I got confused. I'm not sure how to get the sides equal now. I tried a few things...not sure if they're right... I don't know how to make a -cos

^{2}x into cos

^{2}x and same with the sin.

multiplied in order to get common denominators

(cos

^{2}x-sin

^{2}x)/sinxcosx = (sin

^{2}x-cos

^{2}x)/sinxcosx