Question

If $\sin y=x\sin (a+y)$ , then show

$\frac{dy}{dx}=\frac{\sin (a+y)}{\cos y-x.\cos (a+y)}$

Answer 1

Given ,

$\sin y=x.\sin (a+y)$

$Differentiatewithrespecttoyweget$

$\cos y=x\cos (a+y)+\sin (a+y).\frac{dx}{dy}$

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

$\frac{dy}{dx}=\frac{\sin (a+y)}{\cos y-x.\cos (a+y)}$