Prove the identity:

Question

1-cos2x/sin2x = 1+tanx/1+cotx

I simplified the RS to tanx.
LS:(1-2cos²x+1)/2sinxcosx
(2+2cos²x)/2sinxcosx

How do I simplify the rest?

Answer 1

change the LS to
(1 - (1 - 2sin²x))/(2sinxcosx)
= 2sin²x/(2sinxcox)
= sinx/cosx
= tanx = RS

Answer 2

thanks! I've been trying to get this one for quite awhile. So many options to choose :(