CVT1

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Verify the identity: \sin(a\pm b)=\sin(a)\cos(b)\pm \cos(a)\sin(b)\,

Since \sin(a)={\frac  {e^{{ai}}-e^{{-ai}}}{2i}},\cos(b)={\frac  {e^{{bi}}+e^{{-bi}}}{2}}\,

These two products can be computed:

\sin(a)\cos(b)={\frac  {e^{{i(a+b)}}+e^{{i(a-b)}}-e^{{-i(a-b)}}-e^{{-i(a+b)}}}{4i}}\,

\cos(a)\sin(b)={\frac  {e^{{i(a+b)}}-e^{{i(a-b)}}+e^{{-i(a-b)}}-e^{{-i(a+b)}}}{4i}}\,

\sin(a)\cos(b)+\cos(a)\sin(b)={\frac  {2e^{{i(a+b)}}-2e^{{-i(a+b)}}}{4i}}=\sin(a+b)\,

\sin(a)\cos(b)-\cos(a)\sin(b)={\frac  {2e^{{i(a-b)}}-2e^{{-i(a-b)}}}{4i}}=\sin(a-b)\,


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