You can put this solution on YOUR website! How do you contract: sin^2(4pi/9)-cos^2(4pi/9)?
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In general, sin^2(x)-cos^2(x)
= sin^2(x)-[1-sin^2(x)]
= 2sin^2(x)-1
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Your Problem:
sin^2(4pi/9)-cos^2(4pi/9)
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= 2sin^2[4pi/9]-1
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Cheers,
Stan H.