Question

If ${\sin }^{-1}x+{\sin }^{-1}y=\frac{\pi }{2}$, then $\frac{dy}{dx}$ is equal to

• A. $\frac{x}{y}$
• B. $-\frac{x}{y}$
• C. $\frac{y}{x}$
• D. $-\frac{y}{x}$

Answer 1

The correct option is B $-\frac{x}{y}$

Given ${\sin }^{-1}x+{\sin }^{-1}y=\frac{\pi }{2}$
$\Rightarrow {\sin }^{-1}x=\frac{\pi }{2}-{\sin }^{-1}y$
$\Rightarrow {\sin }^{-1}x={\cos }^{-1}y$
$\Rightarrow y=\sqrt{1-x^2}$
$\frac{dy}{dx}=\frac{1}{2\sqrt{1-x^2}}(-2x)$
$\Rightarrow \frac{dy}{dx}=-\frac{x}{y}$