Cos Pi 4 Theta 2

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Cos Pi 4 Theta 2
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https://latex.codecogs.com/png.latex?\bg_white cos(\frac\pi4+\theta )=cos(\frac\pi4)cos\theta -sin(\frac\pi4)sin\theta \\cos(\frac\pi4-\theta )=cos(\frac\pi4)cos\theta +sin(\frac\pi4)sin\theta \\2cos(\frac\pi4+\theta )cos(\frac\pi4-\theta )=2[cos(\frac\pi4)cos\theta -sin(\frac\pi4)sin\theta][cos(\frac\pi4)cos\theta +sin(\frac\pi4)sin\theta ] \\=2(\frac12cos^2\theta-\frac12sin^2\theta) \\=cos^2\theta -sin^2\theta \\=cos(2\theta )