• anonymous
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  • Owlfred
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  • watchmath
Recall that \(\cos(2x)=2\cos^2(x)-1\) Plugin \(x=\theta/2\) we have \(1+\cos(\theta)=2\cos^2(\theta/2)\). When you take the square root of that you get \(\sqrt{2}\sqrt{\cos^2(\theta/2)}\) and then this the two square roots become \(2\) in the front of the integral.

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