Question

How do you simplify this expression step by step using trigonometric identities?

Answer 1

$\bf \textit{Pythagorean Identities}\\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(\theta )cos^2(\theta )+tan^2(\theta )\implies \cfrac{1}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} +tan^2(\theta ) \\\\\\ 1+tan^2(\theta )\implies sec^2(\theta )$