Rewriting cos

**abc10** · January 25th 2011, 01:30 PM

How would I rewrite cos3theta in terms of costheta any help would be much appreciated!

**dwsmith** · January 25th 2011, 01:32 PM

Originally Posted by abc10

How would I rewrite cos3theta in terms of costheta any help would be much appreciated!

$\cos(2x+x)=\cos(2x)\cos(x) - \sin(2x)\sin(x)=\cdots$

**Archie Meade** · January 25th 2011, 01:47 PM

Originally Posted by abc10

How would I rewrite $cos3\theta$ in terms of $cos\theta$ any help would be much appreciated!

$Cos3\theta=Cos(2\theta+\theta)$

$Cos(A+B)=CosACosB-SinASinB$

$\Rightarrow\ Cos3\theta=Cos2\theta\ Cos\theta-Sin2\theta\ Sin\theta$

$Cos2A=Cos^2A-Sin^2A$

$Sin2A=2SinACosA$

$Sin^2A=1-Cos^2A$

$\Rightarrow\ Cos3\theta=\left[Cos^2\theta-Sin^2\theta\right]Cos\theta-2Sin\theta\ Cos\theta\ Sin\theta$

$=Cos^3\theta-\left(1-Cos^2\theta\right)Cos\theta-2\left(1-Cos^2\theta\right)Cos\theta$

**abc10** · January 25th 2011, 01:52 PM

You guys rock!

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