观察下面各等式的结构规律,提出一个猜想________.
(1)sin210°+sin250°+sin10°?sin50°=0.75
(2)sin26°+sin254°+sin6°?sin54°=0.75
(3)sin222°+sin238°+sin22°?sin38°=0.75
(4)sin215°+sin245°+sin15°?sin45°=0.75.
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解:观察等式 (1)sin210°+sin250°+sin10°?sin50°=0.75,
(2)sin26°+sin254°+sin6°?sin54°=0.75,
(3)sin222°+sin238°+sin22°?sin38°=0.75,
(4)sin215°+sin245°+sin15°?sin45°=0.75,
照此规律,可以得到的一般结果应该是
sin2α+sin2(60°-α)+sinα?sin(60°-α)=.
故