已知函数f(x)=cosx^2-sinx^2+2sinxcosx 当x属于【-π/4,π/4】,求f(x)的最值及相应的x值
问题描述:
已知函数f(x)=cosx^2-sinx^2+2sinxcosx 当x属于【-π/4,π/4】,求f(x)的最值及相应的x值
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答
f(x)=cosx^2-sinx^2+2sinxcosx=cos2x+sin2x=√2(√2/2*cos2x+√2/2*sin2x)=√2(sin2xcosπ/4+cos2xsinπ/4)=√2(sin2x+π/4)x∈[-π/4,π/4]2x∈[-π/2,π/2]2x+π/4∈[-π/4,3π/4]当2x+π/4=-π/4时 ,即x=-π/4时,...