Question

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

• A. No solution
• B. One solution
• C. Two solutions
• D. Three solutions

Answer 1

The correct option is A No solution

$2co{s}^{-1}x+si{n}^{-1}x=\frac{11\pi }{6}$
$\therefore co{s}^{-1}x=\frac{11\pi }{6}-\frac{\pi }{2}$ Since $[si{n}^{-1}x+co{s}^{-1}x=\frac{\pi }{2}]$
$co{s}^{-1}x=\frac{8\pi }{6}=\frac{4\pi }{3}$
But range of $co{s}^{-1}xϵ[0,\pi ]$
So, this equation has no solution.