show that $$ \cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\\ \text{ if } AB=BA $$
the question gives a hint to use: $$ \sin(A)=\frac{1}{2i}(e^{iA}-e^{-iA})\\ \cos(A)=\frac{1}{2}(e^{iA}+e^{-iA}) $$
show that $$ \cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\\ \text{ if } AB=BA $$
the question gives a hint to use: $$ \sin(A)=\frac{1}{2i}(e^{iA}-e^{-iA})\\ \cos(A)=\frac{1}{2}(e^{iA}+e^{-iA}) $$