CBSE Class 12 · 2020 · Inverse Trigonometric FunctionsMultiple Choice

Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).
Assertion (A): Domain of $y={\cos }^{-1}(x)$ is $[-1,1]$.
Reason (R): The range of the principal value branch of $y={\cos }^{-1}(x)$ is $[0,\pi ]-\left\{\frac{\pi }{2}\right\}$.

If $a={\sin }^{-1}\left(\frac{\sqrt{2}}{2}\right)+{\cos }^{-1}\left(-\frac{1}{2}\right)$ and $b={\tan }^{-1}(\sqrt{3})-{\cot }^{-1}\left(-\frac{1}{\sqrt{3}}\right)$, then find the value of $a+b$.

A statement of Assertion (A) is followed by a statement of Reason (R).
Assertion (A): Maximum value of ${\left({\cos }^{-1}x\right)}^2$ is ${\pi }^2$.
Reason (R): Range of the principal value branch of ${\cos }^{-1}x$ is $\left[-\frac{\pi }{2},\frac{\pi }{2}\right]$.

Evaluate ${\sin }^{-1}\left(\sin \frac{3\pi }{4}\right)+\cos \left({\cos }^{-1}\pi \right)+{\tan }^{-1}1$.

Draw the graph of ${\cos }^{-1}x$, where $x\in [-1,0]$. Also write its range.

Prove that ${\sin }^{-1}\left(2x\sqrt{1-x^2}\right)=2{\cos }^{-1}x,\frac{1}{\sqrt{2}}\le x\le 1$.