Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

$\mathrm{A}={\left({\tan }^{-1}\mathrm{x}\right)}^3+{\left({\cot }^{-1}\mathrm{x}\right)}^3$ for $\mathrm{x}>0;\mathrm{B}={\left({\cos }^{-1}\mathrm{t}\right)}^2+{\left({\sin }^{-1}\mathrm{t}\right)}^2$ for $0\le \mathrm{t}\le 1/\sqrt{2}$. Use ${\tan }^{-1}\mathrm{x}+{\cot }^{-1}$ $\mathrm{x}=\pi /2$ and ${\sin }^{-1}\mathrm{t}+{\cos }^{-1}\mathrm{t}=\pi /2$ on these domains.