If $\sin x=-\frac{3}{5}$, where $\pi

Question

If $\sin x=-\frac{3}{5}$, where $\pi<x<\frac{3 \pi}{2}$, then $80\left(\tan ^2 x-\cos x\right)$ is equal to [JEE Main 2024, 8 Apr (Shift 1)]

YESPYQ · Accepted Answer

Correct answer: a) 109. $\sin x=\frac{-3}{5},\pi \(\Rightarrow \tan x=\frac{3}{4}$ and $\cos x=-\frac{4}{5}$ $80\left({\tan }^{2}x-\cos x\right)=80\left(\frac{9}{16}+\frac{4}{5}\right)=45+64=109$

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

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If \(\sin x=-\frac{3}{5}\), where \(\pi&lt;x&lt;\frac{3 \pi}{2}\), then \(80\left(\tan ^2 x-\cos x\right)\) is equal to …

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