Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Let ${\mathrm{t}}_1$ be $\left({\sin }^{-1}\mathrm{x}\right)$ to the power $\left({\sin }^{-1}\mathrm{x}\right)$; ${\mathrm{t}}_2$ be $\left({\sin }^{-1}\mathrm{x}\right)$ to the power $\left({\cos }^{-1}\mathrm{x}\right)$; ${\mathrm{t}}_3$ be $\left({\cos }^{-1}\mathrm{x}\right)$ to the power $\left({\sin }^{-1}\mathrm{x}\right)$; and ${\mathrm{t}}_4$ be $\left({\cos }^{-1}\mathrm{x}\right)$ to the power $\left({\cos }^{-1}\mathrm{x}\right)$. Match each interval in List I to the decreasing order in List II. List I: (A) $\mathrm{x}\in (0,\cos 1)$; (B) $\mathrm{x}\in (\cos 1,1/\sqrt{2})$; (C) $\mathrm{x}\in (1/\sqrt{2},\sin 1)$; (D) $\mathrm{x}\in (\sin 1,1)$. List II: (P) ${\mathrm{t}}_1>{\mathrm{t}}_2>{\mathrm{t}}_4>{\mathrm{t}}_3$; (Q) ${\mathrm{t}}_4>{\mathrm{t}}_3>{\mathrm{t}}_1>{\mathrm{t}}_2$; (R) ${\mathrm{t}}_2>{\mathrm{t}}_1>{\mathrm{t}}_4>{\mathrm{t}}_3$; (S) ${\mathrm{t}}_3>{\mathrm{t}}_4>{\mathrm{t}}_1>{\mathrm{t}}_2$.