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Thread: cotangent

  1. #1
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    cotangent

    Can I distribute cotangent here???

    cot(Arccot 3 + Arccot 7 + Arccot 15 + Arccot 21)

    Can you please show the solution???
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  2. #2
    Super Member
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    Quote Originally Posted by maeca View Post
    Can I distribute cotangent here???

    cot(Arccot 3 + Arccot 7 + Arccot 15 + Arccot 21)

    Can you please show the solution???
    nope you cannot distribute the cotangent here, you will need to use the double angle formula here (several times)

    first note that $\displaystyle \cot ( A + B ) = \frac{\cot A \cot B - 1}{\cot A + \cot B}$

    so your thing becomes

    $\displaystyle \cot( accot 3 + acot 7 + acot 15 + acot 21) = \frac{\cot (accot 3 + acot 7) \cot (acot 15 + acot 21) - 1}{\cot (accot 3 + acot 7) + \cot (acot 15 + acot 21)}
    $

    can you finish this off ?

    Bobak
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