How do you solve (1+cosx)(1-cosx) /(tanx)=sinxcosx?

Question

This is a trigonometry identity problem. 

Answer 1

OK, Mark, let's do this thing.

 

First, (1 + cosx)(1 - cosx) = 1 - cos²x = sin²x

 

tanx = sinx/cosx

 

So, we have sin²x/(sinx/cosx) = sin²x(cosx/sinx) = (sin²xcosx)/sinx

 

sinx cancels out, so we are left with sinxcosx.

 

Hope this helps!

Answer 2

(1+cosx)(1-cosx)/(tanx)=sinxcosx

(1+cosx)(1-cosx)=1-cos²x=sin²x

tanx=sinx/cosx

substitute

sin²x/(sinx/cosx)

sinxsinx/(sinx/cosx)

sinx/(1/cosx)

sinxcosx