The value of sin − 1 ( sin 10 ) is, 10, 10 − 3 π, 3 π − 10, None of these

⇒ Since 3 π 10 3 π + 2 π ⇒ 0 10 − 3 π 2 π 2 − π 3 π − 10 0 ⇒ sin − 1 { sin ( 3 π − 10 )} = 3 π − 10

The value of sin − 1 ( sin 10 ) is

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The value of $\sin ^{-1}(\sin 10)$ is

MathematicsInverse Trigonometric FunctionsJEE Main

Options:

A $10$
B $10-3 \pi$
C $3 \pi-10$
D None of these

Solution:

2122 Upvotes Verified Answer

The correct answer is: $3 \pi-10$

$\begin{aligned} & \text{Since } 3 \pi \lt 10 \lt 3 \pi+\frac{\pi}{2} \Rightarrow 0 \lt 10-3 \pi \lt \frac{\pi}{2} \\ \Rightarrow & \frac{-\pi}{2} \lt 3 \pi-10 \lt 0 \Rightarrow \sin ^{-1}\{\sin (3 \pi-10)\}=3 \pi-10\end{aligned}$

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