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Q.
The equation $2\, cos^{-1} x+ sin^{-1} x = \frac{11\pi}{6}$ has
Inverse Trigonometric Functions
Solution:
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 $cos^{-1}x \in\left[0,\,\pi\right]$.