# The value of the expression $2\sec^{-1}2+\sin^{-1}\frac{1}{2}$ is:

$(A)\quad\frac{\pi}{6}\quad(B)\quad\frac{5\pi}{6}\quad(C)\quad\frac{7\pi}{6}\quad(D)\quad 1$

Toolbox:
• $$sin^{-1}\large\frac{1}{2}=\large\frac{\pi}{6},$$
• $$sec^{-1}2=\large\frac{\pi}{3}$$
Ans (B) $$\large\frac{5\pi}{6}$$

Substituting the above values we get
$$2.\large\frac{\pi}{3}+\large\frac{\pi}{6}=\large\frac{5\pi}{6}$$

answered Feb 18, 2013
edited Mar 16, 2013