Consider the following inequalities :<br>1. \sin 1^\circ \lt \cos 57^\circ<br>2. \cos 60^\circ \gt \sin 57^\circ<br>Which of the above is/are correct?

Explanation

Since \cos 57^\circ = \sin 33^\circ, the first inequality is \sin 1^\circ \lt \sin 33^\circ, which is true as sine is strictly increasing in (0, 90^\circ). For the second, \cos 60^\circ = \sin 30^\circ, so it asks if \sin 30^\circ \gt \sin 57^\circ, which is false. Thus, only 1 is correct.

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