How do you verify (1-cos2t)/ sin t= 2 sin t?

May 13, 2015

use the fact that $\cos 2 t = {\cos}^{2} t - {\sin}^{2} t$ to get
$\frac{1 - {\cos}^{2} t + {\sin}^{2} t}{\sin} t = 2 \sin t$
But $1 = {\sin}^{2} t + {\cos}^{2} t$
So:
$\frac{{\sin}^{2} t + \cancel{{\cos}^{2} t} - \cancel{{\cos}^{2} t} + {\sin}^{2} t}{\sin} t = 2 \sin t$
$\frac{2 {\sin}^{\cancel{2}} t}{\cancel{\sin t}} = 2 \sin t$

$2 \sin t = 2 \sin t$