Question

Solve identity,
(1-sin2x)/cos2x = cos2x/(1+sin2x)

I tried starting from the right side,
RS:
=(cos²x-sin²x)/(1+2sinxcosx)
=(cos²x-(1-cos²x))/(1+2sinxcosx)

and the right side just goes in circle. May I get a hint to start off?

Answer 1

First of all since the angle is 2x throughout, let's just use y for 2x
Secondly, you probably want to prove it as an identity, rather than solve it

RS
= cosy/(1+siny)<b> [(1-siny)/(1-siny)]</b>
= cosy(1-siny)/(1- sin^2 y)
= cosy(1-siny)/cos^2y
= (1-siny)/cosy)
= (1- sin 2x)/cos 2x
= LS

Answer 2

Cross multiply.

cos^2(2x) = 1- sin^2(2x) = cos^2 2x
q.e.d.

x can be anything.

That is why it is called an identity

Answer 3

Got it, thanks!