Question

Simplify:
${\sin }^{3}x{\cos }^{3}x$

Answer 1

We have,

${\sin }^{3}x{\cos }^{3}x$

On multiplying and divide by 8 and we get,

$\frac{8}{8}{\sin }^{3}x{\cos }^{3}x$

$\Rightarrow \frac{1}{8}{\left(2\sin x\cos x\right)}^3$

$\Rightarrow \frac{1}{8}{\left(\sin 2x\right)}^3$

$\Rightarrow \frac{1}{8}{\sin }^{3}2x$.