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

$2{\cos }^{-1}x+{\sin }^{-1}x=\frac{11\pi }{6}$
${\cos }^{-1}x+\frac{\pi }{2}=\frac{11\pi }{6}$ ($\because {\cos }^{-1}x+{\sin }^{-1}x=\frac{\pi }{2}$)
${\cos }^{-1}x=\frac{11\pi }{6}-\frac{\pi }{2}=\frac{11\pi -3\pi }{6}=\frac{8\pi }{6}=\frac{4\pi }{3}\notin [0,\pi ]$
$\Rightarrow$ Given equation has no solution