Product to Sum Formulas
s i n ( u ) s i n ( v ) = 1 2 [ c o s ( u − v ) − c o s ( u + v ) ] {\displaystyle sin(u)sin(v)={\frac {1}{2}}[cos(u-v)-cos(u+v)]}
c o s ( u ) c o s ( v ) = 1 2 [ c o s ( u − v ) + c o s ( u + v ) ] {\displaystyle cos(u)cos(v)={\frac {1}{2}}[cos(u-v)+cos(u+v)]}
s i n ( u ) c o s ( v ) = 1 2 [ s i n ( u + v ) + s i n ( u − v ) ] {\displaystyle sin(u)cos(v)={\frac {1}{2}}[sin(u+v)+sin(u-v)]}
c o s ( u ) s i n ( v ) = 1 2 [ s i n ( u + v ) − s i n ( u − v ) ] {\displaystyle cos(u)sin(v)={\frac {1}{2}}[sin(u+v)-sin(u-v)]}
Sum to Product Formula
s i n ( u ) + s i n ( v ) = 2 s i n ( u + v 2 ) c o s ( u − v 2 ) {\displaystyle sin(u)+sin(v)=2sin({\frac {u+v}{2}})cos({\frac {u-v}{2}})}
s i n ( u ) − s i n ( v ) = 2 c o s ( u + v 2 ) s i n ( u − v 2 ) {\displaystyle sin(u)-sin(v)=2cos({\frac {u+v}{2}})sin({\frac {u-v}{2}})}
c o s ( u ) + c o s ( v ) = 2 c o s ( u + v 2 ) c o s ( u − v 2 ) {\displaystyle cos(u)+cos(v)=2cos({\frac {u+v}{2}})cos({\frac {u-v}{2}})}
c o s ( u ) − c o s ( v ) = − 2 s i n ( u + v 2 ) s i n ( u − v 2 ) {\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
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