Q75 / 150 · MHT CET 2026 (16 April Shift 1) · Mathematics

$\cos\left(\cos^{-1}\left(-\dfrac{1}{2}\right) + \dfrac{\pi}{3}\right) =$

  • A
    $0$
  • Correct answer
    B
    $-1$
  • C
    $1$
  • D
    $\dfrac{1}{2}$

Solution

The principal value branch of $\cos^{-1}(x)$ is $[0, \pi]$.

We know that $\cos\left(\dfrac{2\pi}{3}\right) = -\dfrac{1}{2}$.

Therefore, $\cos^{-1}\left(-\dfrac{1}{2}\right) = \dfrac{2\pi}{3}$.

Substituting this into the given expression:

$\cos\left(\cos^{-1}\left(-\dfrac{1}{2}\right) + \dfrac{\pi}{3}\right) = \cos\left(\dfrac{2\pi}{3} + \dfrac{\pi}{3}\right)$

$= \cos(\pi)$

$= -1$

Answer: $-1$

Hence, the correct answer is option: 'B'.

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