Inverse Trigonometric Functions Question 27
Question: The sum of the solutions of the equation $ 2{{\sin }^{-1}}\sqrt{x^{2}+x+1}+{{\cos }^{-1}}\sqrt{x^{2}+x}=\frac{3\pi }{2} $ is
Options:
A) 0
B) -1
C) 1
D) 2
Show Answer
Answer:
Correct Answer: B
$ 0\le x^{2}+x+1\le 1 $ and $ 0\le x^{2}+x+\le 1 $
$ \therefore x=-1,0 $ For $ x=-1 $ L.H.S. $ =2{{\sin }^{-1}}1+{{\cos }^{-1}}0=\frac{3\pi }{2} $
$ \therefore x=-1 $ is a solutions. For $ x=0, $ L.H.S. $ =2{{\sin }^{-1}}1+{{\cos }^{-1}}0=\frac{3\pi }{2} $
Therefore, $ x=0 $ is a solution and sum of the solutions $ =-1 $ .
BETA
