Question

cos^4(3x) - sin^4(3x)

Answer 1

You need to use the following: \[ \begin{array}{rcl}
a^2-b^2 &=& (a-b)(a+b) &\text{Difference of squares} \\
1 &=& \sin^2(x)+\cos^2(x) &\text{Pythagorean Theorem} \\
\cos(2x) &=& \cos^2(x) - \sin^2(x)&\text{Double angle formula}
\end{array}
\]