# 1-secx

Input |
---|

1 – sec(x) |

Alternate form assuming x is real |

1 – (2 cos(x))/(cos(2 x) + 1) |

Roots |

x = 2 pi n, n element Z |

Series expansion at x=0 |

-x^2/2 – (5 x^4)/24 – (61 x^6)/720 + O(x^7) (Taylor series) |

Derivative |

d/dx(1 – sec(x)) = tan(x) (-sec(x)) |

Indefinite integral |

integral (1 – sec(x)) dx = x + log(cos(x/2) – sin(x/2)) – log(sin(x/2) + cos(x/2)) + constant |

Local maxima |

max{1 – sec(x)} = 0 at x = 2 pi n for integer n |

Local minima |

min{1 – sec(x)} = 2 at x = 2 pi n + pi for integer n |