Question

The equation $2co{s}^{-1}x+si{n}^{-1}x=\frac{11\pi }{6}$ has

• A. no solution
• B. only one solution
• C. two solutions
• D. three solutions

Answer 1

Answer: (A)

Given equation is $2co{s}^{-1}x+si{n}^{-1}x=\frac{11\pi }{6}$
$\Rightarrow co{s}^{-1}x+\left(co{s}^{-1}x+si{n}^{-1}x\right)=\frac{11\pi }{6}$
$\Rightarrow co{s}^{-1}x+\frac{\pi }{2}=\frac{11\pi }{6}$
$\Rightarrow co{s}^{-1}x=\frac{4\pi }{3}$
which is not possible as $co{s}^{-1}x\in \left[0,\pi \right]$.