Prove by vector method that `sin(A-B)=sinAcosB-cosAsinB` and `sin(A+B)=sinAcosB+cosAsinB`

Explanation

Here, `vecc(OP) = vecai + vecbj`



`Vec and vecc(OQ) = vecci + dj`


Now,` OP × OQ = (veca vecd – vecb vecc)k`


`[(OP)(OQ)sin(POQ)] = (veca vecd – vecb vecc)k`


`-sin(VECA − VECB) = (veca vecd – vecb vecc)/(vec(OP)vec(OQ))`


`= (veca/(OP)).(vecd/(OQ)).(vecb/(OP)).(vecc/(OQ))`


`= cosA.sinB - sinA.cosB`


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