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Trig Identities 2
Sum, diff, product, power
Term | Definition |
---|---|
sin(u±v) | sin u cos v ± cos u sin v |
cos(u±v) | cos u cos v ±' sin u sin v |
tan(u±v) | tan u ± tan v / 1 ±' tan u tan v |
sin(2u) | 2 sin u cos u |
cos(2u) | cos²u-sin²u or 2cos²u - 1 or 1-2sin²u |
tan(2u) | 2 tan u / 1 - tan²u |
sin²u | 1/2[1-cos(2u)] |
cos²u | 1/2[1+cos(2u)] |
tan²u | 1 - cos(2u) / 1 + cos(2u) |
sin u + sin v | 2 sin (u+v/2) cos (u-v/2) |
sin u - sin v | 2 cos (u+v/2) sin (u-v/2) |
cos u + cos v | 2 cos (u+v/2) cos (u-v/2) |
cos u - cos v | -2 sin (u+v/2) sin (u-v/2) |
sin u sin v | 1/2 [cos(u-v) - cos(u+v)] |
cos u cos v | 1/2[cos(u-v) + cos(u+v)] |
sin u cos v | 1/2[sin(u+v) + sin (u-v)] |
cos u sin v | 1/2[sin(u+v) - sin (u-v)] |
sin (u/2) | sqrt (1-cosu / 2) |
cos (u/2) | sqrt (1+cosu / 2) |
tan (u/2) | (1-cosu)/sinu or sinu/(1+cosu) |