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化简sin4x%sin2x+Cos2x=

原式=1?[(sin2x+cos2x)2?3sin2xcos2x]sin2x+3sin2x=3sin2xcos2xsin2x+3sin2x=3cos2x+3sin2x=3(sin2x+cos2x)=3.故答案为:3

cos4x-sin2x=1-2sin²2x-sin2x

因为:cos4x+sin4x+sin2xcos2xsin6x+cos6x+2sin2xcos2x=(sin 2x+cos 2x) 2?2sin 2xcos 2x +sin 2xcos 2x (sin 2x+cos 2x) [(sin 2x) 2?sin 2xcos 2x+(cos 2x ) 2]+ 2sin 2xcos 2x =1?sin 2xcos 2x (sin 2x) 2+(cos 2x) 2+sin 2xcos 2x =1?sin 2x...

原式=-sin^2x(1-sin^2x)+cos^2x =-(1-cos^2x)*cos^2x+cos^2x =-cos^2x+cos^4x+cos^2x =cos^4x

cos4x=cos²2x-sin²2x=cos2x+sin2x (cos2x+sin2x)(cos2x-sin2x)-(cos2x+sin2x)=0 (cos2x+sin2x)(cos2x-sin2x-1)=0 cos2x+sin2x=0,cos2x-sin2x=1 cos2x+sin2x=0 √2sin(2x+π/4)=0 2x+π/4=kπ x=kπ/2-π/8 cos2x-sin2x=1 sin2x-cos2x=-1 √2s...

请采纳 谢谢 f(x)=(sin^4+cos^4+sin^2xcos^2x)/2-sin2x =((sin^2x+cos^2x)^2-sin^2xcos^2x)/2-sin2x =(1-sin^2xcos^2x)/2-sin2x =(1-sin2x平方/4)/2-sin2x =(20-(sin2x+4)^2)/8 最小正周期π;最大11/8;最小-5/8

代数式才化简,方程不化简。

sin2x=2sinxcosx,这是sin的二倍角公式, “sin2x乘cos2x为什么等于1/2sin4x"题中只是将x替换为2x 就是 sin(2*2x)=2sin2xcos2x 即sin2xcos2x=1/2sin4x

方法1: 原式=∫sin⁴x cos²x =∫sin⁴x (1 - sin²x) dx =∫(sin⁴x - sin^6x) dx = ∫sin⁴x dx - ∫sin^6x dx 后面的看附图,自己整理吧 方法2: 原式=∫sin⁴x cos²x dx =∫sin²x (sinxcosx)² dx...

记住基本公式 sin2x=2sinxcosx 所以得到(sinx)^2 *(cosx)^2 =1/4 *(2sinxcosx)^2 =1/4 *(sin2x)^2,就是你要的结果

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