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 $[0, \pi]-\left\{\frac{\pi}{2}\right\}$

$$\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$$ is equal to:

Find value of $k$ if $\sin ^{-1}\left[k \tan \left(2 \cos ^{-1} \frac{\sqrt{3}}{2}\right)\right]=\frac{\pi}{3}$.

Write the domain and range (principle value branch) of the following functions: $$f(x)=\tan ^{-1} x$$