Question

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

• A. one
• B. two
• C. three
• D. zero

Answer 1

Answer: (B)

$\because {\left(\sin x\right)}^{-1}=\frac{1}{\sin x}=\text{cosec}x$
Now, from graphs of ${\sin }^{-1}x,\text{cosec}x$

Clearly, both graph intersects at two points
$\therefore$ two solutions