Question

Verify the identity. Show your work. 1 + sec^2xsin^2x = sec^2x

Answer 1

$\bf \textit{Pythagorean Identities} \\\\ 1+tan^2(\theta)=sec^2(\theta)\\\\ -------------------------------\\\\ 1+sec^2(x)sin^2(x)=sec^2(x) \\\\\\ 1+\cfrac{1}{cos^2(x)}\cdot sin^2(x)\implies 1+\cfrac{sin^2(x)}{cos^2(x)}\\\\\\ 1+tan^2(x)\implies sec^2(x)$