Assertion (A): Range of [ sin^-1 x +2 cos^-1 x ] is [0, π]. Reason ( R ): Principal value branch of sin^-1 x has range [-(π)/2, (π)/2].

Assertion (A) : Range of $\displaystyle \left[\sin ^{-1} \mathrm{x}+2 \cos ^{-1} \mathrm{x}\right]$ is $\displaystyle [0, \pi]$. Reason ( $\displaystyle R$ ) : Principal value branch of $\displaystyle \sin ^{-1} \mathrm{x}$ has range $\displaystyle \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.