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

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

Apply pythagorean identity.

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

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

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

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

Multiply $2$ by $2$ .

$\tan^{4} (x)$