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 $\sin^{-1}y=\frac{\pi}{2}-\sin^{-1}x$, $y=\cos(\sin^{-1}x)=\sqrt{1-x^2}$, so $\sqrt{1-y^2}=x$ and $\sqrt{1-x^2}=y$. Hence $\frac{dy}{dx}=-\frac{x}{y}$.