Question

Find the value of \(\cos^{-1}\Big(\dfrac12\Big)+2\sin^{-1}\Big(\dfrac12\Big)\).

Hint:

Use the standard values cos^-1(1/2)=pi/3 and sin^-1(1/2)=pi/6.

Answer 1

Step 1: Key Formula or Approach:
\(\cos^{-1}\big(\tfrac12\big)=\dfrac{\pi}{3}\) and \(\sin^{-1}\big(\tfrac12\big)=\dfrac{\pi}{6}\), both standard values.

Step 2: Substituting:
\(\cos^{-1}\big(\tfrac12\big)+2\sin^{-1}\big(\tfrac12\big)=\dfrac{\pi}{3}+2\times\dfrac{\pi}{6}=\dfrac{\pi}{3}+\dfrac{\pi}{3}\).

Final Answer:
\[ \boxed{\dfrac{2\pi}{3}} \]