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

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Inverse Trigonometric Functions

x = sin^{- 1} (sin 10)

and

y = cos^{- 1} (cos 10)

, then

y - x

is equal to:

Answer: (A)

Both arguments are in radians, and

10

lies between

3 π \approx 9.42

and

4 π \approx 12.57

. For

sin^{- 1} (sin 10)

to land in

[- \frac{π}{2}, \frac{π}{2}]

, use

x = 3 π - 10

. For

cos^{- 1} (cos 10)

to land in

[0, π]

, use

y = 4 π - 10

. Then

y - x = (4 π - 10) - (3 π - 10) = π

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