1. ## Identities

Can anyone help me change $[4cos^4(x/2)]/tan^2 x$ into $cos^2 x/[tan^2(x/2)]$ ?

Thanks.

2. $\tan x=\frac{2\tan\frac{x}{2}}{1-\tan^2\frac{x}{2}}$

Then $\tan^2x=\frac{4\tan^2\frac{x}{2}}{\left(1-\tan^2\frac{x}{2}\right)^2}=4\tan^2\frac{x}{2}\cdo t\frac{\cos^4\frac{x}{2}}{\cos^2x}$

$\frac{4\cos^4\frac{x}{2}}{\tan^2x}=\frac{4\cos^4\f rac{x}{2}}{4\tan^2\frac{x}{2}}\cdot\frac{\cos^2x}{ \cos^4\frac{x}{2}}=\frac{\cos^2x}{\tan^2\frac{x}{2 }}$