# Trig Identity

## Homework Statement

Prove:
cosA/(1-tanA) + sinA/(1-cotA) = sinA + cosA

I have tryed turning tan and cot into sin and cos and everything but I can not prove it... can some one help??
Thank you.

## The Attempt at a Solution

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Dick
Homework Helper
Not until you show what you did that didn't work.

cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)

Dick
Homework Helper
cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)
That's good! Now (cos^2-sin^2)=(cos-sin)*(cos+sin), right? Just multiply it out.

O wow, I dont know why I ddint notice that.... I think I have been studying to long ha...

Mentallic
Homework Helper
cos/(1-sin/cos)+ sin/(1-cos/sin)
cos^2/(cos-sin) + sin^2/(sin-cos)
(cos^2 - Sin^2)/(cos-sin)
I'm very impressed! It hass been a long time since the precalculus forum has seen any consistently correct algebraic manipulations from a student in just 1 post!

Thank you... I just started doing them yesterday.