Question

Find the value of cos-1$(\frac{1}{2})$+2 sin-1$(\frac{1}{2})$

Answer 1

Let cos-1$(\frac{1}{2})=x.$
Then, $cos \, x=\frac {1}{2}=cos\frac{\pi}{3}.$
therefore cos-1$(\frac{1}{2})=\frac{\pi}{3}$
Let sin-1$(\frac{1}{2})=y.$
Then $sin\,y=\frac{1}{2}=sin\,\frac{\pi}{6}$
therefore sin-1$(\frac{1}{2})=\frac{\pi}{6}$

so cos-1$(\frac{1}{2})$+2 sin-1$(\frac{1}{2})=\frac{\pi}{3}+\frac{2\pi}{6}=\frac{2\pi}{3}$