Question

prove that cos x. cos (y-x) -sinx. (y-x) =cos y​

Answer 1

Answer:

Given,

cosy=xcos(a+y)

x=cos(a+y)cosy

differentiating w.r.t x, we get,

dxd(x)=dxd(cos(a+y)cosy)

1=dyd(cos(a+y)cosy)×dxdy

1=(cos2(a+y)sin(a+y)cosy−cos(a+y)siny)×dxdy

1=(cos2(a+y)sin((a+y)−y))×dxdy

1=cos2(a+y)sinadxdy

∴dxdy=sin