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[tex]cos^{2} \alpha -4sin^{2} \frac{ \alpha }{2} cos^{2} \frac{ \alpha }{2} [/tex]
[tex]cos^{2} \alpha -4sin^{2} \frac{ \alpha }{2} cos^{2} \frac{ \alpha }{2} [/tex]
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(2sin(a/2)cos(a/2))^2 = (sina)^2(cosa)^2 - (sina)^2 = cos(2a)