Question

If $si{n}^{-1}x+si{n}^{-1}y=\frac{\pi }{2}$, 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

Answer: (B)

$-\frac{x}{y}$

Given that,

$si{n}^{-1}x+si{n}^{-1}y=\frac{\pi }{2}$

$\therefore si{n}^{-1}x=co{s}^{-1}y$

$\Rightarrow y=\sqrt{1-x^2}$

On differentiating with respect to x, we get

$\frac{dy}{dx}=\frac{-2x}{2\sqrt{1-x^2}}=-\frac{x}{y}$