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# Trigonometric Id.

### Formula

Theorems/Properties | Formulas/Definitions |
---|---|

Even/Odd Identities. | cos (-u) = cos(u) and sec(-u) = sec(u). the remaining 4 are odd functions. |

Sum and difference identities for cosine. | cos(a+b) = cos(a)cos(b) - sin(a)sin(b). cos(a-b) = cos(a)cos(b) + sin(a)sin(b). |

Sum and difference identities for sine. | sin(a+b) = sin(a)cos(b) + cos(a)sin(b). sin(a-b) = sin(a)cos(b) - cos(a)sin(b). |

Cofunction identities. | cos(pi/2 - u) = sin(u) and sin(pi/2 - u) = cos(u). sec(pi/2 - u) = csc(u) and csc(pi/2 - u) = sec(u). tan(pi/2 - u) = cot(u) and cot(pi/2 - u) = tan(u). |

Double angle identity. | cos(2x) = cos² - sin²(x). sin(2x) = 2*sin(x)cos(x). tan(2x) = (2*tan(x))/(1 - tan²(x)). |

Power reduction formulas. | cos²(x) = (1/2)*(1 + cos(2x)). sin²(x) = (1/2)*(1 - cos(2x)). |

Half angle formulas. | cos(x/2) = -/+ sqrt[(1/2)*(1 + cos(x))]. sin(x/2) = -/+ sqrt[(1/2)*(1 - cos(x))]. tan(x/2) = -/+ sqrt[(1 - cos(x))/(1 + cos(x))]. |

Sum to product formulas. | cos(a) + cos(b) = 2*cos[(1/2)*(a + b)]*cos[(1/2)*(a - b)]. cos(a) - cos(b) = -2*sin[(1/2)*(a + b)]*sin[(1/2)*(a - b)]. sin(a) +/- sin(b) = 2*sin[(1/2)*(a +/- b)]*cos[(1/2)*(a -/+ b)]. |

Product to sum formulas. | cos(a)cos(b) = (1/2)*[cos(a - b) + cos( a + b)]. sin(a)sin(b) = (1/2)*[cos(a - b) - cos(a + b)]. sin(a)cos(b) = (1/2)*[sin(a - b) + sin(a + b)]. |