JEE PYQ: Inverse Trigonometric Functions Question 18
Question 18 - 2019 (09 Jan Shift 2)
If $x = \sin^{-1}(\sin 10)$ and $y = \cos^{-1}(\cos 10)$, then $y - x$ is equal to:
(1) 0
(2) 10
(3) $7\pi$
(4) $\pi$
Show Answer
Answer: (4)
Solution
$x = \sin^{-1}(\sin 10) = 3\pi - 10$ (since $3\pi - \frac{\pi}{2} < 10 < 3\pi + \frac{\pi}{2}$, so $3\pi - x = 10$). And $y = \cos^{-1}(\cos 10) = 4\pi - 10$ (since $3\pi < 10 < 4\pi$, so $4\pi - x = 10$). Therefore $y - x = (4\pi - 10) - (3\pi - 10) = \pi$.
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