Question

Find the value of $\sin \left(\frac{1}{2}{\cot }^{-1}(-\frac{3}{4})\right)$.

Answer 1

$\begin{array}{c}\sin \left(\frac{1}{2}{\cot }^{-1}\left(\frac{-3}{4}\right)\right)\\ let\frac{1}{2}{\cot }^{-1}\left(\frac{-3}{4}\right)=\theta \\ {\cot }^{-1}\left(\frac{-3}{4}\right)=2\theta \\ \cot 2\theta =\frac{-3}{4}\\ \therefore \tan 2\theta =\frac{-4}{3}\\ Then\sin \left(\theta \right)=\frac{-2}{\sqrt{1}3}\end{array}$