JEE Main 2023TrigonometryTrigonometric Ratio and IdentitesMediumQuestionIf sinx=−35\sin x=-\frac{3}{5}sinx=−53, where π<x<3π2\pi< x <\frac{3 \pi}{2}π<x<23π, then 80(tan2x−cosx)80\left(\tan ^2 x-\cos x\right)80(tan2x−cosx) is equal toOptionsA109B108C19D18Check AnswerHide SolutionSolutionsinx=−35 where π<x<3π2tanx=34,cosx=−45∴80(tan2x−cosx)=80(916+45)=80(45+6480)=109\begin{aligned} & \sin x=-\frac{3}{5} \text { where } \pi < x < \frac{3 \pi}{2} \\ & \qquad \tan x=\frac{3}{4}, \cos x=\frac{-4}{5} \\ & \therefore 80\left(\tan ^2 x-\cos x\right) \\ & =80\left(\frac{9}{16}+\frac{4}{5}\right) \\ & =80\left(\frac{45+64}{80}\right) \\ & =109 \end{aligned}sinx=−53 where π<x<23πtanx=43,cosx=5−4∴80(tan2x−cosx)=80(169+54)=80(8045+64)=109