# How do you prove that  2cos^4x + 2sin^2xcos^2x = cos2x + sin^2x+cos^2x ?

Jul 15, 2018

Here ${\cos}^{2} x + {\sin}^{2} x = 1$

The question provided by you now can be written as:-

$2 \cos x + 2 {\sin}^{2} x {\cos}^{2} x = \cos 2 x + 1$

$\implies$ $2 {\cos}^{4} x + 2 {\sin}^{2} x {\cos}^{2} x$

$\implies$ Now taking $2 {\cos}^{2} x$ common we get,

$\implies$ $2 {\cos}^{x} \left({\cos}^{2} x + {\sin}^{2} x\right)$

$\implies$ Now this equation becomes, $2 {\cos}^{2} x$

$\implies$ This can be written as:- $\cos 2 x + 1$