Question

if siny= xsin(a+y),then prove that dy/dx=sin^2(a+y)/sin a

Answer 1

sin(x−y)=sinx.cosy−siny.cosx
It's very simple here. You just have to separate out the terms containing x and terms containing y:-

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

So how it is derived.

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