Hi again fellow math gurus (minus "fellow")!

I'm trying to prove that:

1) sin(pi/2 - x) = sin(pi/2 + x)

This is how I went about it...

RHS = sin(pi/2) cos x + cos(pi/2) sin x

= (1) cos x

= cos x

I know that doesn't exactly work out and I'm stumped hahaha!

2) This one is more recent:

(2 tan x)/(1+tan^2 x) = sin 2x

I'm not looking for the answer so much as maybe a hint at what identities to start with? I tried going about it couple different ways but this stuff is just greek to me hehe. I'm trying to get really good at it before my final exam in 3 weeks.

Thanks for the continued support!