Question Number 113825 by deepraj123 last updated on 15/Sep/20
$$\mathrm{The}\:\mathrm{greatest}\:\mathrm{and}\:\mathrm{least}\:\mathrm{values}\:\mathrm{of} \\ $$$$\left(\mathrm{sin}^{−\mathrm{1}} {x}\right)^{\mathrm{3}} +\:\left(\mathrm{cos}^{−\mathrm{1}} {x}\right)^{\mathrm{3}} \:\:\mathrm{are} \\ $$
Answered by MJS_new last updated on 15/Sep/20
$$\frac{\pi^{\mathrm{3}} }{\mathrm{32}}\leqslant\left(\mathrm{sin}^{−\mathrm{1}} \:{x}\right)^{\mathrm{3}} +\left(\mathrm{cos}^{−\mathrm{1}} \:{x}\right)^{\mathrm{3}} \leqslant\frac{\mathrm{7}\pi^{\mathrm{3}} }{\mathrm{32}} \\ $$