Prove the identity.

Question

sin² θ = tan² θ / 1 + tan² θ

Answer 1

I assume the right side is supposed to be tan² è /(1 + tan² è)

Start by rewriting
1 + tan^2 = (cos^2 + sin^2)/cos^2
= 1 /cos^2
so that
1/(1+tan^2) = cos^2
Therefore the right side becomes
(sin^2/cos^2)* cos^2 = sin^2

Answer 2

how did 1 + tan^2 become cos^2 + sin ^2?

Answer 3

oh nevermind i got it thank you.

Answer 4

we know sec^2(x)-tan^2(x)=1
now sec^2(x)=1+tan^2(x)
now tan^2(x)/sec^2(x)=sin^2(x) [tan(x)=sin(x)/cos(x)]
[sec(x)=1/cos(x)]