Inverse Trigonometric Functions Question 56
Question: $ {{\sin }^{-1}}\frac{1}{\sqrt{5}}+{{\cot }^{-1}}3 $ is equal to
[MP PET 1993; Karnataka CET 1995]
Options:
A) $ \frac{\pi }{6} $
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{3} $
D) $ \frac{\pi }{2} $
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Answer:
Correct Answer: B
Solution:
$ {{\sin }^{-1}}\frac{1}{\sqrt{5}}+{{\cot }^{-1}}3={{\cot }^{-1}}( \frac{\sqrt{1-\frac{1}{5}}}{\frac{1}{\sqrt{5}}} )+{{\cot }^{-1}}3 $
$ ={{\cot }^{-1}}(2)+{{\cot }^{-1}}(3)={{\cot }^{-1}}( \frac{2\times 3-1}{3+2} )={{\cot }^{-1}}(1)=\frac{\pi }{4} $ .
BETA
