Question

How do you use the Pythagorean identity to solve this?

Answer 1

`\bf \textit{Pythagorean Identities} \\ \quad \\ \boxed{sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)} \\ \quad \\ 1+cot^2(\theta)=csc^2(\theta) \\ \quad \\ 1+tan^2(\theta)=sec^2(\theta) \\\\\\ and\qquad \qquad tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\\\\ -----------------------------\\\\`


`\bf tan(\theta)[1-sin^2(\theta)]=sin(\theta)cos(\theta)\\\\ -----------------------------\\\\ tan(\theta)\boxed{cos^2(\theta)}\implies \cfrac{sin(\theta)}{cos(\theta)}\cdot cos^2(\theta) \implies sin(\theta)cos(\theta)`