若sinθ+sin^2θ=1,则cos^2θ+cos^4θ+cos^6θ

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/05 01:54:48
若sinθ+sin^2θ=1,则cos^2θ+cos^4θ+cos^6θ
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若sinθ+sin^2θ=1,则cos^2θ+cos^4θ+cos^6θ
若sinθ+sin^2θ=1,则cos^2θ+cos^4θ+cos^6θ

若sinθ+sin^2θ=1,则cos^2θ+cos^4θ+cos^6θ
sinθ+sin^2θ=1,sin^2θ+cos^2θ=1
∴sinθ=cos^2θ
等式两边同时乘以sinθ有
sin^2θ+sin^3θ=sinθ
∴sin^3θ=sinθ-sin^2θ=cos^2θ-sin^2θ=cos2θ
∴
=sinθ+sin^2θ+sin^3θ
=1+sin^3θ
=1+cos2θ
=2cos^2θ
=2sinθ
根据sin²θ+sinθ-1=0
解出sinθ=（-1±根号5）/2,带入就行了

sinθ+sin^2θ=1
sinθ=1-sin^2θ=cos^2θ
所以原式=sinθ+sin^2θ+sin^3θ
=sinθ+sinθ(sinθ+sin^2θ)
=sinθ+sinθ
=2sinθ

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