Question

The equation $2{\cos }^{-1}x+{\sin }^{-1}x=\frac{11\pi }{6}$ has

• A. No solution
• B. only one solution
• C. Two solutions
• D. Three solutions

Answer 1

The correct option is A No solution

$2{\cos }^{-1}x+{\sin }^{-1}x=\frac{11\pi }{6}\Rightarrow {\cos }^{-1}x+\frac{\pi }{2}=\frac{11\pi }{6}(\because {\cos }^{-1}x+{\sin }^{-1}x=\frac{\pi }{2})\Rightarrow {\cos }^{-1}x=\frac{11\pi }{6}-\frac{\pi }{2}\Rightarrow {\cos }^{-1}x=\frac{4\pi }{3}\notin [0,\pi ]$

Hence, there is no solution.