JEE MAIN - Mathematics (2024 - 8th April Morning Shift - No. 16)

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
109
108
19
18

Explanation

$$\begin{aligned} & \sin x=-\frac{3}{5} \text { where } \pi < x < \frac{3 \pi}{2} \\ & \qquad \tan x=\frac{3}{4}, \cos x=\frac{-4}{5} \\ & \therefore 80\left(\tan ^2 x-\cos x\right) \\ & =80\left(\frac{9}{16}+\frac{4}{5}\right) \\ & =80\left(\frac{45+64}{80}\right) \\ & =109 \end{aligned}$$

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