Question

The value of $\cos^{-1}(\frac{-1}{2}) + \cos^{-1}(\frac{1}{2})$ is

• A. 0
• B. $\frac{\pi}{3}$
• C. $\frac{\pi}{6}$
• D. $\pi$

Answer 1

Answer: (D)

$\pi$

Answer 2

We know that:

$$\cos^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} \quad \text{and} \quad \cos^{-1}\left(\frac{-1}{2}\right) = \frac{2\pi}{3} \quad (\text{in } [0,\pi]).$$

Thus, the sum is:

$$\frac{2\pi}{3} + \frac{\pi}{3} = \pi.$$