若sinθ+sin^2θ=1,则cos^2θ+cos^4θ+cos^6θ
问题描述：
若sinθ+sin^2θ=1,则cos^2θ+cos^4θ+cos^6θ
答
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
答
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...