The power reducing formula for the fourth power of the cosine function is:
[tex]\cos ^4\theta=\frac{3}{8}+\frac{1}{2}\cos (2\theta)+\frac{1}{8}\cos (4\theta)[/tex]
Replace θ=3x to find the expression for cos⁴(3x) in terms of the first power of the cosine function:
[tex]\begin{gathered} \cos ^4(3x)=\frac{3}{8}+\frac{1}{2}\cos (2\cdot3x)+\frac{1}{8}\cos (4\cdot3x) \\ \frac{3}{8}+\frac{1}{2}\cos (6x)+\frac{1}{8}\cos (12x) \end{gathered}[/tex]
Therefore, the answer is:
[tex]\cos ^4(3x)=\frac{3}{8}+\frac{1}{2}\cos (6x)+\frac{1}{8}\cos (12x)[/tex]
Use the second option to write this expression as input.
