The greatest value of sin⁴θ + cos⁴θ 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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Important Questions from Trigonometry
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If p sin A − cos A = 1, then p2 − (1 + p2) cos A equals:
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Find the value of cot 15°
