# Proof this, please?

1 - (sin^2x tanx/(tanx+1)) - (cos^2x/(tanx+1)) = sinx cosx

Show your work. Please don't skip any steps.

### 2 Answers

Relevance

- Saurabh DubeyLv 42 years agoFavorite Answer
LHS = 1 - [ (sin²x tanx ) / (tanx + 1) ] -

[ cos²x / (tanx + 1) ]

= [( tanx + 1) - sin²x tanx - cos²x ] / (tanx + 1)

= [ (tanx - sin²x tanx) + ( 1 - cos²x ) ] / (tanx+1)

= [ tanx ( 1 -sin²x) + sin²x ] / (tanx + 1)

= ( tanx cos²x + sin²x ) / (tanx +1)

=[ (sinx / cosx ) cos²x + sin²x ] /

[ (sinx /cosx) + 1 ]

= [ sinx cosx + sin²x ] / [ (sinx + cosx)/cosx]

= sinx ( cosx + sinx) / [ (sinx + cosx)/cosx]

= sinx cosx = RHS........ proved

I hope this helps !

Source(s): Note: ● 1- sin²x = cos²x ● 1- cos²x = sin²x ● tanx = sinx / cosx - ?Lv 62 years ago
I proofed what you posted.

All appears in order, except the grammar.

I think you want someone to prove the proof provided.

Still have questions? Get your answers by asking now.

I DON'T CARE. IT'S MATH HOMEWORK NOT ENGLISH HOMEWORK IF YOU CAN'T TELL.