Inverse Trigonometric Functions Question 228
Question: If $ {{\tan }^{-1}}x+2{{\cot }^{-1}}x=\frac{2\pi }{3}, $ then x =
[Karnataka CET 1999]
Options:
A) $ \sqrt{2} $
B) 3
C) $ \sqrt{3} $
D) $ \frac{\sqrt{3}-1}{\sqrt{3}+1} $
Show Answer
Answer:
Correct Answer: C
Solution:
The given equation may be written as $ {{\tan }^{-1}}x+{{\cot }^{-1}}x+{{\cot }^{-1}}x=\frac{2\pi }{3} $
Therefore $ {{\cot }^{-1}}x=\frac{2\pi }{3}-\frac{\pi }{2} $ = $ \frac{\pi }{6} $
Therefore $ x=\sqrt{3} $ .
BETA
