Evaluate \( \cos \left[ \cos^{-1} \left( \frac{-\sqrt{3}}{2} \right) + \frac{\pi}{6} \right] \)
NCERT, Ex. 2.3, Q.2, Page 35
Solution:
We have,
\[ \cos \left[ \cos^{-1} \left( \frac{-\sqrt{3}}{2} \right) + \frac{\pi}{6} \right] = \cos \left[ \cos^{-1} \left( \cos \frac{5\pi}{6} \right) + \frac{\pi}{6} \right] \]
\[ = \cos \left( \frac{5\pi}{6} + \frac{\pi}{6} \right) \]
\[ = \cos \left( \frac{6\pi}{6} \right) \]
\[ = \cos(\pi) = -1 \]
Final Answer:
\[ \boxed{-1} \]
Keywords: cos[cos-1((-√3)/2) + π/6], evaluate cos inverse expression, NCERT class 12 trigonometry Q2 Ex 2.3, trigonometric identities solutions