Inverse Trigonometric Functions Question 45
Question: For the equation $ {{\cos }^{-1}}x+{{\cos }^{-1}}2x+\pi =0 $ , the number of real solution is
[Orissa JEE 2005]
Options:
A) 1
B) 2
C) 0
D) $ \infty $
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{\cos }^{-1}}x+{{\cos }^{-1}}(2x)=-\pi $
Therefore $ {{\cos }^{-1}}2x=-\pi -{{\cos }^{-1}}x $
$ \Rightarrow 2x=\cos (\pi +{{\cos }^{-1}}x) $
Therefore $ 2x=\cos \pi (\cos {{\cos }^{-1}}x)-\sin \pi \sin ({{\cos }^{-1}}x) $
$ 2x=-x\Rightarrow x=0 $ But $ x=0 $ does not satisfy the given equation. No solution will exist.
BETA
