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

Number 5 is 50 degreesnumber 6 is 45 degreesnumber 7 is 60 degreesnumber 8 is 45 degrees