#trigonometry

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marsh sluice
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novel plaza
# marsh sluice

Take u = arcsin(x). The the left side becomes u^3 + (π/2 - u)^3. So, find the extrema of that function for |u| ≤ π/2.

marsh sluice
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How you wrote 1-u?

novel plaza
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Alright, done.

marsh sluice
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So our function is u^3+(π/2-u)^3 =kπ^3

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For extreme double derivative?

novel plaza
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Well, only the left side. We can find its extrema as usual.

novel plaza
marsh sluice
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Closed interval

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How did you get it?

novel plaza
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What? There's no integration here.

marsh sluice
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first derivative will be 3u^2-3(π/2-u)
u^2-(π/2-u)
U^2+u-π/2

marsh sluice
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@novel plaza