If sin⁻¹ x + sin⁻¹ y = π/2, then (dy)/(dx) is equal to

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

Correct option: (b)

Answer: (b) $-\frac{x}{y}$ Differentiating: $\frac{1}{\sqrt{1-x^2}} + \frac{1}{\sqrt{1-y^2}}\frac{dy}{dx} = 0$. Since $\sin^{-1}y = \frac{\pi}{2} - \sin^{-1}x$, $y = \cos(\sin^{-1}x) = \sqrt{1-x^2}$ and $\sqrt{1-y^2} = x$. Hence $\frac{dy}{dx} = -\frac{x}{y}$.