Question

Use the sum formula for sine to show that sin(???? − ????) = sin(????)cos(????) − cos(????)sin(????).

Answer 1

Answer and explanation :

We have to prove
`sin(A-B)=sinAcosB-cosAsinB` by using sum formula

We know that
`sin(A+B)=sinAcosB+cosAsinB`

Now replace B = -B

So
`sin(A+(-B))=sinAcos(-B)+cosAsin(-B)`

We know that
`cos(-B)=cos(B)\ and \ and\  sin(-B)=-sinB`

So
`sin(A-B)=sinAcosB-cosAsinB` which we have to prove