Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Put t=${\sin }^{-1}x\in [-\pi /2,\pi /2]$. The expression t³+($\pi /2-t$)³ is a convex quadratic with vertex t=$\pi /4$, minimum ${\pi }^3/32$. The endpoint t=-$\pi /2$ gives maximum 7${\pi }^3/8$.