# Simplify trigonometric function in terms of tangent

• August 3rd 2012, 05:53 AM
shiny718
Simplify trigonometric function in terms of tangent
Simplify $(4 \cos^2 9^\circ -3)(4\cos^2 27^\circ -3 )$ in terms of tangent.
• August 3rd 2012, 06:10 AM
Prove It
Re: Simplify trigonometric function in terms of tangent
Quote:

Originally Posted by shiny718
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*}
• August 3rd 2012, 07:14 AM
shiny718
Re: Simplify trigonometric function in terms of tangent
Sorry but I tried to use your hint but I couldn't get anywhere. Help please?
• August 3rd 2012, 07:16 AM
Prove It
Re: Simplify trigonometric function in terms of tangent
Quote:

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 \begin{align*} \cos^2{x} \equiv \frac{1}{1 + \tan^2{x}} \end{align*}.

Replace your square cosine terms with this.
• August 3rd 2012, 09:05 AM
shiny718
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?