Question

Prove the identity. sec to the power of 2 x (1- sin to the power of 2 x) =1

Answer 1

`\bf sec(\theta)=\cfrac{1}{cos(\theta)} \\\\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ sec^2(x)[1-sin^2(x)]=1\\\\ -------------------------------\\\\ \textit{checking the left-hand-side}\\\\ \cfrac{1^2}{cos^2(x)}[cos^2(x)]\implies 1`