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MHTCET 16 Apr 2026 Shift 1 Paper

Question : 117 of 150

Marks: +1, -0

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

Solution:

Concept:

Use the principal value of

\cos^{-1} x

and simplify the angle inside

\cos

Explanation:

The principal value range of

\cos^{-1} x

[0, \pi]

Since

\cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2}

, we get:

\cos^{-1}\left(-\frac{1}{2}\right) = \frac{2\pi}{3}

Now substitute this value into the given expression:

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

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

Therefore:

\cos(\pi) = -1

Hence, the correct answer is Option B:

-1

Answer:

-1

(Option B)

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