# Csc(2x)

Input |
---|

csc(2 x) |

Alternate form assuming x is real |

-(2 sin(2 x))/(cos(4 x) – 1) |

Roots |

(no roots exist) |

Series expansion at x=0 |

1/(2 x) + x/3 + (7 x^3)/45 + (62 x^5)/945 + O(x^6) (Laurent series) |

Derivative |

d/dx(csc(2 x)) = -2 cot(2 x) csc(2 x) |

Indefinite integral |

integral csc(2 x) dx = -1/2 log(cot(x)) + constant |

Local maxima |

max{csc(2 x)} = -1 at x = pi n – pi/4 for integer n |

Local minima |

min{csc(2 x)} = 1 at x = pi n + pi/4 for integer n |