# How do you prove cos4x=1-2sin^2(2x)?

Jan 8, 2016

using trig. identities.

#### Explanation:

by using double angle formula .

we can write that $\cos 4 x = {\cos}^{2} 2 x - {\sin}^{2} 2 x$

if we use the identity that ${\cos}^{2} 2 x = 1 - {\sin}^{2} 2 x$

then placing this into the above gives

$\cos 4 x = \left(1 - {\sin}^{2} 2 x\right) - {\sin}^{2} 2 x$

removing the bracket gives

$\cos 4 x = 1 - {\sin}^{2} 2 x - {\sin}^{2} 2 x$

$\Rightarrow \cos 4 x = 1 - 2 {\sin}^{2} 2 x$