Exams › SSC CGL (Prelims) › General

If \(\sin\theta - \cos\theta = 0\) for an acute angle \(\theta\), then find the value of \(\sin^4\theta + \cos^4\theta\).

1. 1
2. 1/2
3. 3/4
4. 1/4

Correct answer: 1/2

Solution

From \(\sin\theta - \cos\theta = 0\), we get \(\sin\theta = \cos\theta\). Since \(\theta\) is acute, \(\theta = 45^\circ\), so \(\sin\theta = \cos\theta = 1/\sqrt{2}\). Then \(\sin^4\theta + \cos^4\theta = 2\left(\frac{1}{2}\right)^2 = \frac{1}{2}\).

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