Question

How to simplify sinθ(1+cot^2 θ)

Answer 1

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