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
If A is an acute angle and tanA + cotA = 2, find the value of 7tan⁸A – 6cot⁸A + 8sec²A.
If p = sinA / (1 + cosA), then sinA / (1 - cosA) is equal to:
In a ΔABC, right-angled at B if tanC = √3, then find (sin²C + cos²C) / (1 + cot²C).
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