Question

prove that sin(x-y) cosx - cos(x-y)sin x = -siny​

Answer 1

here is your ans..........

Answer 2

Answer:

Step-by-step explanation:

sin(x-y)cosx-cos(x-y)sinx= -sin y

let us take x-y as a

Therefore

sin a(cos x)- cos a(sin x)= sin a(cos x) - sin(90-a)(cos 90-x)

let us first resolve the second term

sin(90-a)(cos 90-x)= sin(90-x+y)(cos 90- x)

sin a(cos x)= cos(90-x+y)(sin 90-x)

therfore

sin(90-x+y)(cos(90-x)- cos(90-x+y)(sin 90-x)