# Math Help - Proving identities.

1. ## Proving identities.

{1-cos(2t)}/{cos(t)sin(t)} = 2tan(t)

and

{1/(1-sin(t))} + {1/(1+sin(t))} = 2sec^2(t)

2. ## Re: help with trig problems please!!!

Do you know that $\cos{2x}=\cos^2{x}-\sin^2{x}$?

Prove $\frac{1-\cos{2t}}{\cos(t)\sin(t)}=2\tan{t}$
In $\frac{1-\cos{2t}}{\cos(t)\sin(t)}$, substitute $\cos{2t}=\cos^2{t}-\sin^2{t}$ and $1=\cos^2{t}+\sin^2{t}$

$\\ \frac{1-\cos{2t}}{\cos(t)\sin(t)}=\frac{\cos^2{t}+\sin^2{t }-\cos^2{t}+\sin^2{t}}{\cos(t)\sin(t)}=\frac{2\sin^2 {t}}{\sin{t}\cos{t}}=2\frac{\sin{t}}{\cos{t}} \\\\= 2\tan{t}$

Prove $\frac{1}{1-\sin{t}}+\frac{1}{1+\sin{t}}=2\sec^2{t}$
Note that : $\frac{1}{1-\sin{t}}+\frac{1}{1+\sin{t}}=\frac{1+\sin{t}+1-\sin{t}}{(1-\sin{t})(1+\sin{t})}=\frac{2}{1-\sin^2{t}}$

Substitute: $1-\sin^2{t}=\cos^2{t}$ and you will get the answer.