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sinα+sinβ=1 ------>sinα=1-sinβ .cosα+cosβ=0---->cosα=-cosβ 平方相加1=(1-sinβ)²;+(-cosβ)²;=2-2sinβ sinβ=1/2,sinα=1/2 所以cos2α+cos2β=1-2sin²;α+1-2 sin²;β=2-2*(1/4)-2*(1/4)=1
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