Question

Simplify 1-sin squared theta over cos squared theta

Answer 1

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