Verified Solution • 2025–26 Session moderate

QJEEM24Ma760d: JEE Main 2024 Mathematics - Class 11 JEEM24Ma760d Solution: If , where , then is equal to

If sin⁡x=−35\sin x=-\frac{3}{5} , where \pi< x <\frac{3 \pi}{2} , then 80(tan⁡2x−cos⁡x)80\left(\tan ^2 x-\cos x\right) is equal to

Multiple Choice Options

  • A 109
  • B 108
  • C 19
  • D 18

Step-by-Step Verified Solution

amp;sin⁡x=−35 where πlt;xlt;3π2amp;tan⁡x=34,cos⁡x=−45amp;∴80(tan⁡2x−cos⁡x)amp;=80(916+45)amp;=80(45+6480)amp;=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}

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