Question

Prove that cos(A-B) = cos A CosB + Sin A sin B​

Answer 1

To prove:

Cos(A-B)= cosA.cosb+sinA.sinB

LHS: Cos(A-B)

=sin(90-(A-B))  

=sin(90-A+b)

=sin((90-A)+B)    ;  [sin(a+b)=sina.cosb+cosa.sinb]

=sin(90-A).cosB+sinB.cos(90-A)    ;     [sin(90-A)=cosA ; cos(90-A)=sinA]

=cosA.cosB+sinA.sinB

=RHS

∴LHS=RHS, hence proved.