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Product to Sum Formulas
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{\displaystyle sin(u)sin(v)={\frac {1}{2}}[cos(u-v)-cos(u+v)]}
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{\displaystyle cos(u)cos(v)={\frac {1}{2}}[cos(u-v)+cos(u+v)]}
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{\displaystyle sin(u)cos(v)={\frac {1}{2}}[sin(u+v)+sin(u-v)]}
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{\displaystyle cos(u)sin(v)={\frac {1}{2}}[sin(u+v)-sin(u-v)]}
Sum to Product Formula
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{\displaystyle sin(u)+sin(v)=2sin({\frac {u+v}{2}})cos({\frac {u-v}{2}})}
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{\displaystyle sin(u)-sin(v)=2cos({\frac {u+v}{2}})sin({\frac {u-v}{2}})}
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{\displaystyle cos(u)+cos(v)=2cos({\frac {u+v}{2}})cos({\frac {u-v}{2}})}
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{\displaystyle cos(u)-cos(v)=-2sin({\frac {u+v}{2}})sin({\frac {u-v}{2}})}
This material was adapted from the original CK-12 book that can be found here . This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License
![{\displaystyle sin(u)sin(v)={\frac {1}{2}}[cos(u-v)-cos(u+v)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49b9f060b7054ceeb498513300acc3896873419d)
![{\displaystyle cos(u)cos(v)={\frac {1}{2}}[cos(u-v)+cos(u+v)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b5c657f67a82c2a194619f642a34b5f3f7c666)
![{\displaystyle sin(u)cos(v)={\frac {1}{2}}[sin(u+v)+sin(u-v)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4dd3e38489f2f2318957665d6a57024d6393d7f6)
![{\displaystyle cos(u)sin(v)={\frac {1}{2}}[sin(u+v)-sin(u-v)]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0aeb7775ca872f16d7239754d52767bf0d10f005)
