NCERT Class 12 Maths: Evaluate cos[cos⁻¹(−√3/2) + π/6]

NCERT Class 12 Mathematics Solutions – Exercise 2.3 Question 2

NCERT Class 12 Maths | Chapter 2 Inverse Trigonometric Functions

Question

Evaluate \[ \cos\left[\cos^{-1}\left(\frac{-\sqrt{3}}{2}\right) + \frac{\pi}{6}\right] \]

[NCERT Ex 2.3, Question 2, Page 35]

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Solution

We have,

\[ \cos\left[\cos^{-1}\left(\frac{-\sqrt{3}}{2}\right) + \frac{\pi}{6}\right] = \cos\left[\cos^{-1}\left(\cos\frac{5\pi}{6}\right) + \frac{\pi}{6}\right] \]

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\[ = \cos\left(\frac{5\pi}{6} + \frac{\pi}{6}\right) \]

\[ = \cos\left(\frac{6\pi}{6}\right) \]

\[ = \cos(\pi) \]

\[ \boxed{-1} \]