Inverse Trigonometric Functions Question 98
Question: The value of $ {{\sin }^{-1}}{ \cot ( {{\sin }^{-1}}\sqrt{( \frac{2-\sqrt{3}}{4} )}+{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} ) } $ is
Options:
A) 0
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{6} $
D) $ \frac{\pi }{2} $
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Answer:
Correct Answer: A
We have $ {{\sin }^{-1}}{ \cot ( {{\sin }^{-1}}\sqrt{( \frac{2-\sqrt{3}}{4} )}+{{\cos }^{-1}}\frac{\sqrt{12}}{4}+{{\sec }^{-1}}\sqrt{2} ) } $
$ ={{\sin }^{-1}}{ \cot ( {{\sin }^{-1}}\sqrt{{{( \frac{\sqrt{3}-1}{2\sqrt{2}} )}^{2}}}+{{\cos }^{-1}}\frac{\sqrt{3}}{2}+{{\cos }^{-1}}\frac{1}{\sqrt{2}} ) } $
$ ={{\sin }^{-1}}{cot(15{}^\circ +30{}^\circ +45{}^\circ )}=si{n^{-1}}(cot90{}^\circ ) $
$ ={{\sin }^{-1}}0=0 $
BETA
