Inverse Trigonometric Functions Question 195
Question: The equation $ {{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}( \frac{\sqrt{3}}{2} ) $ has
Options:
A) No solution
B) Unique solution
C) Infinite number of solutions
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ {{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\frac{\sqrt{3}}{2}=\frac{\pi }{6} $
But $ {{\sin }^{-1}}x+{{\cos }^{-1}}x=\frac{\pi }{2} $
$ {{\sin }^{-1}}x=\frac{\pi }{3} $ and $ {{\cos }^{-1}}x=\frac{\pi }{6} $
Therefore $ x=\frac{\sqrt{3}}{2} $ is the unique solution.
BETA
