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Trigonometry
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sin4L=4sinLcosL(1-2sin^2L)
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use the cosine and sin double angle formulas cos(2l)=cos^2(l)-sin^2(l)=1-2sin^2(l) sin(2l)=2sinlcosl
sin(20)=sin(10+10)=2sin(10)cos(10)
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