Question

Find the numerical value of one trigonometric function of x if sinxcotx=1/3

Answer 1

$\bf sin(x)cot(x)=\cfrac{1}{3}\implies ~~\begin{matrix} sin(x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ \cfrac{cos(x)}{~~\begin{matrix} sin(x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=\cfrac{1}{3}\implies cos(x) = \cfrac{1}{3} \\\\\\ x = cos^{-1}\left( \cfrac{1}{3} \right)\implies x \approx 70.53^o$