Inverse Trigonometric Functions Question 234
Question: The value of $ {{\cos }^{-1}}( \cos \frac{5\pi }{3} )+{{\sin }^{-1}}( \sin \frac{5\pi }{3} ) $ is
[Roorkee 2000]
Options:
A) 0
B) $ \frac{\pi }{2} $
C) $ \frac{2\pi }{3} $
D) $ \frac{10\pi }{3} $
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Answer:
Correct Answer: A
Solution:
$ {{\cos }^{-1}}( \cos \frac{5\pi }{3} )+{{\sin }^{-1}}( \sin \frac{5\pi }{3} ) $
$ ={{\cos }^{-1}}[ \cos ( 2\pi -\frac{\pi }{3} ) ]+{{\sin }^{-1}}[ \sin ( 2\pi -\frac{\pi }{3} ) ] $
$ =\frac{\pi }{3}-\frac{\pi }{3}=0 $ .
BETA
