Question
The greatest value of sin⁴θ + cos⁴θ is:
This question was previously asked in
SSC CGL 2024 (Tier-I) Previous Year Paper (17-Sep-2024) (Shift 3)
The correct answer is
1
\(\sin^4\theta + \cos^4\theta = (\sin^2\theta + \cos^2\theta)^2 - 2\sin^2\theta\cos^2\theta = 1 - 2\sin^2\theta\cos^2\theta\)
This is maximised when \(\sin^2\theta\cos^2\theta = 0\), i.e., when \(\theta = 0°\) or \(90°\), giving \(\sin^4\theta + \cos^4\theta = 0 + 1 = 1\). Hence the greatest value is 1.
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