Inverse Trigonometric Functions Question 60
Question: If $ {{\cos }^{-1}}\lambda +{{\cos }^{-1}}\mu +{{\cos }^{-1}}\gamma =3\pi , $ then the value of $ \lambda \mu +\mu \gamma +\gamma \lambda $ is
Options:
A) 0
B) 1
C) 3
D) 6
Show Answer
Answer:
Correct Answer: C
We know that $ 0\le {{\cos }^{-1}}x\le \pi . $
Hence, from the question $ {{\cos }^{-1}}\lambda =\pi ,{{\cos }^{-1}}\mu =\pi ,{{\cos }^{-1}}\gamma =\pi $
[ $ \because {{\cos }^{-1}}\lambda +{{\cos }^{-1}}\mu +{{\cos }^{-1}}\gamma =3\pi $ is possible only when each term attains its maximum.]
$ \Rightarrow \lambda =\mu =\gamma =-1\Rightarrow \lambda \mu +\mu \gamma +\gamma \lambda =3. $
BETA
