数学填空题目11.已知cos(7
解：cos(75度+a)=-cos(180-75-a)=-cos(105-a)=-1/3
cos(75度+a)=sin(90-75-a)=sin(15-a)=1/3
sin(a-15)=-1/3
cos(a-15)=±2√2/3
sin(a-105)=sin(a-15-90)=sin(a-15)cos90-cos(a-15)sin90=-cos(a-15)=±2√2/3
cos(105度-a)+sin(a-105度)=-1/3±2√2/3
[-1,0]提示：y=log2[1+cos(π2-α)]+log2[1+sin(π+α)]
=log2(1+sinα)+log2(1-sinα)
=lo...全部
解：cos(75度+a)=-cos(180-75-a)=-cos(105-a)=-1/3
cos(75度+a)=sin(90-75-a)=sin(15-a)=1/3
sin(a-15)=-1/3
cos(a-15)=±2√2/3
sin(a-105)=sin(a-15-90)=sin(a-15)cos90-cos(a-15)sin90=-cos(a-15)=±2√2/3
cos(105度-a)+sin(a-105度)=-1/3±2√2/3
[-1,0]提示：y=log2[1+cos(π2-α)]+log2[1+sin(π+α)]
=log2(1+sinα)+log2(1-sinα)
=log2cos2α
∵α∈[0,π4],22≤cosα≤1,12≤cos2α≤1,
∴－1≤y≤0．
2kπ-π/2≤π/4-2x≤2kπ+π/2
π/2-2kπ≥2x-π/4≥-π/2-2kπ
3π/8-kπ≥x≥-π/8-kπ。
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