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The double angle formulas are
sin (2 theta) = 2 sin theta cos theta
cos (2 theta) = cos ^2 theta - sin ^2 theta
= 2 cos ^2 theta - 1
= 1 - 2 sin ^2 theta
tan ( 2 theta) = 2 tan thets / ( 1 - tan ^2 theta)
We have cos (2 theta) = cos ^2 theta - sin ^2 theta