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