# Math Help - one more identity to prove

1. ## one more identity to prove

Thanks for having a look.

$
\frac{sin2x}{cosx}+\frac{cos2x}{sinx}=cscx
$

2. Originally Posted by nightrider456
Thanks for having a look.

$
\frac{sin2x}{cosx}+\frac{cos2x}{sinx}=cscx
$
$\frac{\sin{2x}}{\cos{x}} + \frac{\cos{2x}}{\sin{x}} = \frac{2\sin{x}\cos{x}}{\cos{x}} + \frac{\cos^2{x} - \sin^2{x}}{\sin{x}}$

$= 2\sin{x} + \frac{\cos^2{x} - \sin^2{x}}{\sin{x}}$

$= \frac{2\sin^2{x} + \cos^2{x} - \sin^2{x}}{\sin{x}}$

$= \frac{\sin^2{x} + \cos^2{x}}{\sin{x}}$

$= \frac{1}{\sin{x}}$

$= \csc{x}$.

3. $\frac{\sin 2x}{\cos x}+\frac{\cos 2x}{\sin x}=\frac{\cos (2x-x)}{\sin (x)\cos (x)}=\csc x.$