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JEE Main 20248 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main 2024 · 8 April · Morning Shift · Mathematics · Trigonometric Ratios & Identities

If x=-(3)/(5) , where π < x < (3 π)/(2) , then 80( ^2 x- x) is...

If sin⁡x=−35\sin x=-\frac{3}{5}, where π<x<3π2\pi < x < \frac{3 \pi}{2}, then $80\left(\tan ^2 x-\cos x\right) is equal to

Options

  1. A108
  2. B109
  3. C18
  4. D19

Correct answer

B. 109

Step-by-step solution

sin⁡x=−35,π<x<3π2tan⁡x=34cos⁡x=−4580(tan⁡2x−cos⁡x)=80(916+45)=45+64=109\begin{aligned} & \sin x=\frac{-3}{5}, \pi < x < \frac{3 \pi}{2} \\ & \tan x=\frac{3}{4} \cos x=-\frac{4}{5} \\ & 80\left(\tan ^2 x-\cos x\right) \\ & =80\left(\frac{9}{16}+\frac{4}{5}\right)=45+64=109\end{aligned}
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