How would I rewrite cos3theta in terms of costheta any help would be much appreciated!
$\displaystyle Cos3\theta=Cos(2\theta+\theta)$
$\displaystyle Cos(A+B)=CosACosB-SinASinB$
$\displaystyle \Rightarrow\ Cos3\theta=Cos2\theta\ Cos\theta-Sin2\theta\ Sin\theta$
$\displaystyle Cos2A=Cos^2A-Sin^2A$
$\displaystyle Sin2A=2SinACosA$
$\displaystyle Sin^2A=1-Cos^2A$
$\displaystyle \Rightarrow\ Cos3\theta=\left[Cos^2\theta-Sin^2\theta\right]Cos\theta-2Sin\theta\ Cos\theta\ Sin\theta$
$\displaystyle =Cos^3\theta-\left(1-Cos^2\theta\right)Cos\theta-2\left(1-Cos^2\theta\right)Cos\theta$