Q52 / 90 · JEE Main 2019 (09 Jan Shift 2) · Mathematics

If $x = {s i n}^{- 1} (\sin 10)$ and $y = {c o s}^{- 1} (\cos 10),$ then $y - x$ is equal to:

A
$10$
Correct answer
B
$π$
C
$0$
D
$7 π$

Solution

From the graph of $y = \sin^{- 1} (\sin x),$ it is clear that $\sin^{- 1} (\sin 10) = 3 π - 10$

From the graph of $y = \cos^{- 1} (\cos x)$

It is clear that $\cos^{- 1} (\cos 10) = 4 π - 10$

Hence $y - x = (4 π - 10) - (3 π - 10) = π$

Hence, the correct answer is option: 'B'.

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Solution

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If $x = {s i n}^{- 1} (\sin 10)$ and $y = {c o s}^{- 1} (\cos 10),$ then $y - x$ is equal to: