Inverse Trigonometric Functions Question 235
Question: If $ 4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi , $ then $ x $ is equal to
[UPSEAT 2001]
Options:
A) 0
B) $ \frac{1}{2} $
C) $ -\frac{\sqrt{3}}{2} $
D) $ \frac{1}{\sqrt{2}} $
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Answer:
Correct Answer: B
Solution:
We know that $ 4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi $
Therefore $ 3{{\sin }^{-1}}x+{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi $
Therefore $ 3{{\sin }^{-1}}x=\pi -\frac{\pi }{2}=\frac{\pi }{2} $
Therefore $ {{\sin }^{-1}}x=\pi /6 $
Therefore $ x=\sin \frac{\pi }{6}=\frac{1}{2} $ .
BETA
