# Thread: Simplify trigonometric function in terms of tangent

1. ## Simplify trigonometric function in terms of tangent

Simplify $\displaystyle (4 \cos^2 9^\circ -3)(4\cos^2 27^\circ -3 )$ in terms of tangent.

2. ## Re: Simplify trigonometric function in terms of tangent

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

3. ## Re: Simplify trigonometric function in terms of tangent

Sorry but I tried to use your hint but I couldn't get anywhere. Help please?

4. ## Re: Simplify trigonometric function in terms of tangent

Originally Posted by shiny718
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 \displaystyle \begin{align*} \cos^2{x} \equiv \frac{1}{1 + \tan^2{x}} \end{align*}.

Replace your square cosine terms with this.

5. ## Re: Simplify trigonometric function in terms of tangent

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