# Cot 2x csc 2x

Input |
---|

cot(2 x) csc(2 x) |

Alternate form assuming x is real |

(2 sin(2 x) sin(4 x))/(cos(4 x) – 1)^2 |

Roots |

x = 1/4 (2 pi n + pi), n element Z |

Series expansion at x=0 |

1/(4 x^2) – 1/6 – (7 x^2)/30 – (31 x^4)/189 + O(x^6) (Laurent series) |

Derivative |

d/dx(cot(2 x) csc(2 x)) = -(cos(4 x) + 3) csc^3(2 x) |

Indefinite integral |

integral cot(2 x) csc(2 x) dx = -1/4 csc(x) sec(x) + constant |