Simplify (1-cos(x)^2)^2

${(1 - \cos^{2} (x))}^{2}$

Apply pythagorean identity.

${(\sin^{2} (x))}^{2}$

Multiply the exponents in ${(\sin^{2} (x))}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${\sin (x)}^{2 \cdot 2}$

Multiply $2$ by $2$ .

$\sin^{4} (x)$