Calculus
posted by sh on .
Solve identity,
(1sin2x)/cos2x = cos2x/(1+sin2x)
I tried starting from the right side,
RS:
=(cos²xsin²x)/(1+2sinxcosx)
=(cos²x(1cos²x))/(1+2sinxcosx)
and the right side just goes in circle. May I get a hint to start off?

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) [(1siny)/(1siny)]
= cosy(1siny)/(1 sin^2 y)
= cosy(1siny)/cos^2y
= (1siny)/cosy)
= (1 sin 2x)/cos 2x
= LS 
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 
Got it, thanks!