Exams › SSC CGL (Prelims) › Maths

Let \(0^\circ < t < 90^\circ\). Then which of the following is true?

1. \(\sin t \ne \cos t\) when \(t = 45^\circ\)
2. \(\sin t > \cos t\) when \(t < 45^\circ\)
3. \(\sin t < \cos t\) when \(t < 45^\circ\)
4. \(\sin t < \cos t\) when \(t > 45^\circ\)

Correct answer: \(\sin t < \cos t\) when \(t < 45^\circ\)

Solution

In the first quadrant, \(\sin 45^\circ = \cos 45^\circ\). For angles smaller than \(45^\circ\), sine is less than cosine, and for angles greater than \(45^\circ\), sine becomes greater than cosine. Hence the correct statement is \(\sin t < \cos t\) when \(t < 45^\circ\).

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