Шпаргалка: Тригонометрия

sin(a)+sin(b)=2sin(a+b/2)cos(a-b/2); |

sin(a)-sin(b)=2sin(a-b/2)cos(a+b/2); |

cos(a)+cos(b)=2cos(a+b/2)cos(a-b/2); |

cos(a)-cos(b)=-2cos(a+b/2)cos(a-b/2)= |

=2cos(a+b/2)cos(b-a/2); |

cos(a)+sin(b)=sqrt(2)cos(45-a); |

cos(a)-sin(b)=sqrt(2)sin(45-a); |

tg(a)+tg(b)=sin(a+b)/cos(a)cos(b); |

tg(a)-tg(b)=sin(a-b)/cos(a)cos(b); |

ctg(a)+ctg(b)=sin(a+b)/sin(a)sin(b); |

ctg(a)-ctg(b)=sin(b-a)/sin(a)sin(b); |

tg(a)+ctg(b)=cos(a-b)/cos(a)sin(b); |

tg(a)-ctg(b)=-cos(a+b)/cos(a)sin(b); |

tg(a)+ctg(a)=2/sin(2a); |

tg(a)-ctg(a)=-2ctg(2a); |

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sin(a)sin(b)=1/2(cos(a-b)-cos(a+b)); |

cos(a)cos(b)=1/2(cos(a+b)+cos(a-b)); |

sin(a)cos(b)=1/2(sin(a+b)+sin(a-b)); |

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sin(a)=2tg(a/2)/1+tg^2(a/2); |

cos(a)=1-tg^2(a/2)/1+tg^2(a/2); |

tg(a)=2tg(a/2)/1-tg^2(a/2); |

ctg(a)=1-tg^2(a/2)/2tg(a/2); |