# How do you verify sin^2 theta cos ^2 theta = 1/8 [1-cos(4 theta)]?

Use trig identities: $2 \sin a . \cos a = \sin 2 a$
and $2 {\sin}^{2} a = 1 - \cos 2 a$
${\sin}^{2} a . {\cos}^{2} a$ = $\left(\frac{1}{4}\right) \left({\sin}^{2} 2 a\right)$ = $\left(\frac{1}{8}\right) \left(2 {\sin}^{2} 2 a\right)$ =
$= \left(\frac{1}{8}\right) \left(1 - \cos 4 a\right)$