The set of all x for which sin x ≤ x is

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Question: Answered & Verified by Expert

The set of all $x$ for which $\sin x \leq x$ is

MathematicsTrigonometric EquationsAP EAMCETAP EAMCET 2022 (07 Jul Shift 1)

Options:

A $\left(0, \frac{\pi}{2}\right)$
B $\left(-\frac{\pi}{2}, \pi\right)$
C $\left(\frac{-\pi}{2}, 0\right)$
D $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

Solution:

1444 Upvotes Verified Answer

The correct answer is: $\left(0, \frac{\pi}{2}\right)$

Clearly, $\sin x \leq x$ for $x \in\left(0, \frac{\pi}{2}\right)$

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