Question

if sinx = ysin(x+a)

prove that dy/dx= Sin a/sin^2(x+a)​

Answer 1

Step-by-step explanation:

Sin(x−y)=sinx.cosy−siny.cosx

siny=x.sin(a+y)

x=sinysin(a+y)

Differentiating both sides

dx=sin(a+y).cosy.dy−siny.cos(a+y).dysin2(a+y)

Using Prerequisite (1)

dx=sin(a+y−y).dysin2(a+y)

dx=sina.dysin2(a+y)

So,

dydx=sin^2(a+y)sina