Please suggest suitable approach for this problem
Find the maximum and minimum value of $ \sin ^4 \theta + \cos ^4 \theta $?
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trigonometry
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0In which interval? It's periodic with period $\frac{\pi}{2}$, so it will have a lot of maxima and minima. But if you're restricting to $\left[0,\frac{\pi}{2}\right]$, then it has one minimum and two maxima at the ends. – 2010-11-06
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0I solved it the answer is 1 and 1/2. – 2010-11-06
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2Setting $x=\sin^2\theta$ this reduces to finding the extrema of $x^2+(1-x)^2$ for $x\in[0,1]$. – 2010-11-06
1 Answers
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Note that $$1 = (\sin^2\theta + \cos^2\theta)^2$$ and use $\sin2\theta = 2\sin\theta\cos\theta.$
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0Yes that's the observation ;) – 2010-11-06