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

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

Step 1

Apply pythagorean identity.

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

Step 2

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

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

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

Multiply $2$ by $2$ .

$\cos^{4} (x)$