Question

Prove the equation, you can only change one side csc0-sin0=cot0cos0

Answer 1

$\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ csc(\theta )-sin(\theta )~~ = ~~cot(\theta )cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )-sin(\theta )\implies \cfrac{1}{sin(\theta )}-sin(\theta )\implies \cfrac{1~~ - ~~sin^2(\theta )}{sin(\theta )} \\\\\\ \cfrac{cos^2(\theta )}{sin(\theta )}\implies \cfrac{cos(\theta )}{sin(\theta )}\cdot cos(\theta )\implies cot(\theta )cos(\theta )$