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

Answer: (A)

no solution

Answer 2

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