f(x)=cos4+2sinxcosx-sinx4求最小正周期
问题描述:
f(x)=cos4+2sinxcosx-sinx4求最小正周期
答
f(x)=cos^4x+2sinxcosx-sin^4x=(cos²x+sin²x)(cos²x-sin²x)+sin2x
=cos2x+sin2x
=√2sin﹙2x+π/4﹚
∵T= 2π/2=π
∴f(x)的最小正周期为π.
题目有误吧!应该是 f(x)=cos^4x+2sinxcosx-sin^4x