Question

Verify
tanx + cotx = 1/ sinxcosx

Answer 1

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