S=(cos^2 x+cos^4 x+.+cos^2n x)+(sin^2x+sin^4 x+.+sin^2n x)数列

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S=(cos^2 x+cos^4 x+.+cos^2n x)+(sin^2x+sin^4 x+.+sin^2n x)数列求和题!
答案是(cos^4 x+sin^4 x-cos^2n+4 x-sin^2n+4 x)/sin^2 x.cos^2 x

提示：两个等比数列和,再求和.
S=(cos²x)[1-(cos²x)ⁿ]/(1-cos²x) +(sin²x)[1-(sin²x)ⁿ]/(1-sin²x)
=(cos²x)[1-(cos²x)ⁿ]/sin²x +(sin²x)[1-(sin²x)ⁿ]/cos²x
=[(cos⁴x)-(cosx)^(2n+4)+(sin⁴x)-(sinx)^(2n+4)]/(sin²xcos²x)

证明sin^2(x)+cos^2(x+30)+sin(x)cos(x+30)=3/4 已知tan=2,求(cos x+sin x)/(cos x-sin x)+sin^2x 向量m=(sin ωx+cos ωx,cos ωx)(ω>0),n=(cos ωx-sin ωx,2sin ωx),函数求证（cos^2 x-sin^2 x)(cos^4 x+sin^4 x)+1/4 sin 2x sin 4x=cos 2 sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x) =sin^4x-sin^2xcos 用cos x表示sin^4 x -sin^2 x +cos^2 x 化简[1-(sin^4x-sin^2cos^2x+cos^4x)/(sin^2)]+3sin^2x 求导f(x) = cos(3x) * cos(2x) + sin(3x) * sin(2x). 已知向量m=(根号3sin(x/4),1),向量n=(cos(x/4),cos^2(x/4)) 已知函数f(x)=cos^4 x－2sin x cos x－sin^4 x cos 2x /sin^2 x*cos^2 x不定积分 2cos x (sin x -cos x)+1