[tex]\cos^2(\theta)\cos^2(3\theta)=\frac{1}{2}[/tex]
så langt:
[tex]\cos^2(\theta)\cos^2(3\theta)=\frac{1}{2}\Leftrightarrow \sqrt{\cos^2(\theta)\cos^2(3\theta)}=\sqrt{\frac{1}{2}}\Rightarrow \cos(\theta)\cos(3\theta)=\frac{1}{\sqrt{2}}[/tex]
[tex]\frac{(e^{i\theta}+e^{-i\theta})}{2}\cdot\frac{(e^{i3\theta}+e^{-i3\theta})}{2}=\frac{1}{\sqrt{2}}\Rightarrow \frac{(e^{i4\theta}+e^{-i4\theta})+(e^{i2\theta}+e^{-i2\theta})}{4}=\frac{1}{\sqrt{2}}[/tex]
[tex]\frac{1}{2}\left(\cos(4\theta)+\cos(2\theta)\right)=\frac{1}{\sqrt{2}}\Leftrightarrow \left(\cos(4\theta)+\cos(2\theta)\right) = \sqrt{2}[/tex]
og her stopper det, dessverre
