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  4. The number of solutions of the equation sin- 1x=(sin x)- 1 is/are

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Q. The number of solutions of the equation $sin^{- 1}x=\left(sin x\right)^{- 1}$ is/are

NTA AbhyasNTA Abhyas 2020Inverse Trigonometric Functions

Solution:

$\because \left(sin x\right)^{- 1}=\frac{1}{sin ⁡ x}=cosec ⁡ x$
Now, from graphs of $sin^{- 1} x ,cosec ⁡ x$
Solution
Clearly, both graph intersects at two points
$\therefore $ two solutions