Question

If $x+y=\sin (x-y)$ then $\frac{dy}{dx}$ is equal to

• A. $\frac{1}{2}$
• B. $0$
• C. $-1$
• D. $\frac{1}{3}$

Answer 1

The correct option is C $-1$

Given,

$x+y=\sin (x-y)$

$x+y=\sin x\cos y-\cos x\sin y$

$1+\frac{dy}{dx}=\sin x(-\sin y)+\cos y\left(\cos x\right)-\cos x\left(\cos y\right)-(-\sin x)\sin y$

$1+\frac{dy}{dx}=-\sin x\sin y+\cos x\cos y+\sin x\sin y-\cos x\cos y$

$1+\frac{dy}{dx}=0$

$\therefore \frac{dy}{dx}=-1$