Question

Any help? Simplify cos^2x-cos^4x/tanx

Answer 1

`\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{cos^2(\theta )-cos^4(\theta )}{tan(\theta )}\implies \cfrac{cos^2(\theta )[1-cos^2(\theta )]}{(sin(\theta ))/(cos(\theta ))}\implies \cfrac{cos^2(\theta )[sin^2(\theta )]}{(sin(\theta ))/(cos(\theta ))} \\\\\\ \cfrac{cos^2(\theta )[sin^2(\theta )]}{1} \cdot \cfrac{cos(\theta )}{sin(\theta )}\implies cos^3(\theta )sin(\theta )`