Question

How do you prove `(cosA+cosB)^2+(sinA+sinB)^2=4*cos^2((A-B)/2)`? 2) ?

`(cosA+cosB)^2+(sinA+sinB)^2=4cos^2((A-B)/2)`

Answer 1

`LHS=(cosA+cosB)^2+(sinA+sinB)^2`

`=[2*cos((A+B)/2)*cos((A-B)/2)]^2+[2*sin((A+B)/2)*cos((A-B)/2)]^2`

`=4cos^2((A-B)/2)[sin^2((A+B)/2)+cos^2((A+B)/2)]`

`=4cos^2((A-B)/2)*1=4cos^2((A-B)/2)=RHS`