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θ为锐角,若sinθ+sin2θ=1,则cos2θ+cos^6θ的值为
人气:143 ℃ 时间:2020-05-16 09:44:48
解答

若sinθ+sin²θ=1,θ是锐角

sinθ=1-cos²θ=cos²θ
sinθ=(-1+√5)/2
cos²θ+cos^6θ
=sinθ+sin³θ
=sinθ(1+sin²θ)
=sinθ(1+1-sinθ)
=2sinθ-sin²θ
=2sinθ-(1-sinθ)
=3sinθ-1
=(-5+3√5)/2
谢谢
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