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show that $$ \cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\\ \text{ if } AB=BA $$

the question gives a hint to use: $$ \sin(A)=\frac{1}{2i}(e^{iA}-e^{-iA})\\ \cos(A)=\frac{1}{2}(e^{iA}+e^{-iA}) $$

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    Have you tried multiplying them and using the fact that if $A,B$ commute, then $e^{t (A+B)} = e^{tA} e^{tB} = e^{tB} e^{tA}$ ($t$ is $\pm i$ above)?2012-10-01

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