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Math Help - Simplify trigonometric function in terms of tangent

  1. #1
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    Simplify trigonometric function in terms of tangent

    Simplify  (4 \cos^2 9^\circ -3)(4\cos^2 27^\circ -3 ) in terms of tangent.
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    Re: Simplify trigonometric function in terms of tangent

    Quote Originally Posted by shiny718 View Post
    Simplify  (4 \cos^2 9^\circ -3)(4\cos^2 27^\circ -3 ) in terms of tangent.
    \displaystyle \begin{align*} 1 + \tan^2{x} \equiv \frac{1}{\cos^2{x}}  \end{align*}
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    Re: Simplify trigonometric function in terms of tangent

    Sorry but I tried to use your hint but I couldn't get anywhere. Help please?
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    Re: Simplify trigonometric function in terms of tangent

    Quote Originally Posted by shiny718 View Post
    Sorry but I tried to use your hint but I couldn't get anywhere. Help please?
    Surely you can see from my hint that \displaystyle \begin{align*}  \cos^2{x} \equiv \frac{1}{1 + \tan^2{x}} \end{align*}.

    Replace your square cosine terms with this.
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    Re: Simplify trigonometric function in terms of tangent

    Umm the correct answer I have in hand is  tan 9^\circ . But I can't simplify all my way to this answer. Help me pls?
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