What is the proof the formula for cos (A+B) = cosAcosB-sinAsinB?

Given data, cos (A - B) = cosAcosB + sinAsinB

let, A=60' and B=30' (here the ' sign bears degree)

L. H. S = cos (A - B)

=cos (60'-30) (using value of A and B)

=cos30'

= sqrt3/2

R. H. S = cosAcosB + sinAsinB

=cos60' cos30' + sin60' sin30'

= 1/2 * sqrt3/2 + sqrt3/2*1/2

= sqrt3/4 + sqrt3/4

=2 sqrt3/4

= sqrt3/2

so L. H. S = R. H. S or cos (A - B) = cosAcosB + sinAsinB