JEE Main Previous Year Trigonometry Questions and Solutions - Solution of Triangles trigonometric Identities Question

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Solution

Q.
If $\sin x = - \frac{3}{5},$ where $π < x < \frac{3 π}{2},$ then $80 (\tan^{2} x - \cos x)$ is equal to [2024]

1 109

2 108

3 19

4 18

Ans.
(1)

$\sin x = \frac{- 3}{5},$ $π < x < \frac{3 π}{2}$

$\cos x = \sqrt{1 - \sin^{2} x} = \sqrt{1 - \frac{9}{25}} = \frac{- 4}{5}$ $[$ $∵$ $x$ lies in third quadrant $]$

Now, $\tan x = \frac{3}{4}$

So, $80 (\tan^{2} x - \cos x) = 80 (\frac{9}{16} + \frac{4}{5}) = 45 + 64 = 109$

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