# How do you verify 2 + cos^2 x - 3 cos ^4 x = sin^2 x(2 +3 cos^2 x)?

Mar 8, 2018

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

RHS:

$\left(1 - {\cos}^{2} x\right) \left(2 + 3 {\cos}^{2} x\right)$

$2 - 2 {\cos}^{2} x + 3 {\cos}^{2} x - 3 {\cos}^{4} x$

$2 + {\cos}^{2} x - 3 {\cos}^{4} x$

LHS:

$2 + {\cos}^{2} x - 3 {\cos}^{4} x$

LHS = RHS

Hopefully this helps!