Question Number 10744 by okhema last updated on 24/Feb/17
$${hence}\:{or}\:{otherwise},{solve}\:{the}\:{equation}\:\frac{\mathrm{cosec}\:\theta}{\mathrm{cosec}\:\theta−\mathrm{sin}\:\theta}=\frac{\mathrm{4}}{\mathrm{3}}\:{for}\:\mathrm{0}\leqslant\theta\leqslant\mathrm{2}\Pi \\ $$
Answered by malwaan last updated on 24/Feb/17
$${cox}\:\theta=\pm\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\Rightarrow\theta=\mathrm{30}°\:\:\boldsymbol{{or}}\:\boldsymbol{\theta}=\mathrm{180}−\mathrm{30}=\mathrm{150}° \\ $$$${or}\:\theta=\mathrm{180}+\mathrm{30}=\mathrm{210}°\:{or}\:\theta=−\mathrm{30}° \\ $$$${solutionset}\:=\left\{\mathrm{30};\mathrm{150};\mathrm{210};−\mathrm{30}\right\} \\ $$