高三数学!!
【1】
f(x)=1-2sin²xcos²x+(1/4)√3*sin(4x)
=(1/4)[4-8sin²xcos²x+√3*sin(4x)]
=(1/4)[4-2sin²(2x)+√3*sin(4x)]
=(1/4)[3+cos(4x)+√3*sin(4x)]
=3/4+(1/2)sin(4x+π/6)
4x+π/6=2πk+π/2,4x=2πk+π/3,
f(x=πk/2+π/12)=3/4+1/2=5/4。
【2】
4x+π/6=2πk-π/2,x=πk/2-π/6;
4x+π/6=2πk+3π/2,x=πk/2+π/3。
函数单调递增区间[πk/2-π/6,πk/2+π/12]
单调递减区间[πk/2+π/12,πk/2+π/3]
f(x)=1-2sin²xcos²x+√3/4·sin4x
=1-1/2·sin²2x+√3/4·sin4x
=3/4+1/4·cos4x+√3/4·sin4x
=3/4+1/2·sin(4x+π/3)
故;4x+π/3=2kπ+π/2时,即:x=kπ/2+π/24,k∈Z时,f(x)取得最大值5/4
2kπ-π/2≤4x+π/3≤2kπ+π/2时,即:kπ/2-5π/24≤x≤kπ/2+π/24,k∈Z时,f(x)单调递增
2kπ+π/2≤4x+π/3≤2kπ+3π/2时,即:kπ/2+π/24≤x≤kπ/2+7π/24,k∈Z时,f(x)单调递减
要掌握基础知识才能熟能生巧啊
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