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

[Miike012]

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.

Homework Equations

The Attempt at a Solution

 

[Dick]

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

 

[Miike012]

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

 

[Dick]

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.

 

[Miike012]

O wow, I don't know why I ddint notice that... I think I have been studying to long ha...

 

[Mentallic]

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!

 

[Miike012]

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