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  4. Number of solutions of the equation sin ((1/3) cos-1 x) = 1 are

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Q. Number of solutions of the equation $sin (\frac{1}{3} cos^{-1}\,x) = 1$ are

Inverse Trigonometric Functions

Solution:

$sin(\frac{1}{3} cos^{-1} \,x) = 1$
$\Rightarrow cos^{-1} = \frac{3\pi}{2}$
$\Rightarrow \exists$ no solution, as $x \in [0, \pi]$