Starting with the formula cosA B cos A cos B sin A sin B d

Starting with the formula cos(A + B) = cos A cos B sin A sin B derive the formula cos(A B) = cos A cos B + sin A sin B

Solution

cos(A+B)=cos A cos B -sinA sinB

cos (A-B)=cos(A+(-B) ) = cos A cos(-B)-sinA sin(-B)

And cos(- theta) = cos theta   and sin(- theta)=-sin theta

So we get

cos A cos B - sinA(-sinB) = cos A cos B + sin A sin B

Therefore cos(A-B) = cos A cos B + sinA sinB