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数学
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已知函数f(x)=根号3乘cos2x+2sinxcosx 当x属于[0,2/派]求函数fx的值域
人气:361 ℃ 时间:2019-09-22 09:46:59
解答
∵f(x)=√3*cos2x+2sinxcosx
=√3*cos2x+sin2x
=2(√3/2*cos2x+1/2*sin2x)
=2cos(2x-π/6)
又∵x∈[0,π/2]
∴2x-π/6∈[-π/6,5π/6]
∴f(x)∈[-√3,2]
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