化简 sin(4k-1/4π- α)+cos(4k+1/4π -α)(k∈Z)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/17 06:28:05
化简 sin(4k-1/4π- α)+cos(4k+1/4π -α)(k∈Z)
k是奇数
k=2n-1
则原式=sin(kπ-π/4-a)+cos(kπ+π/4-a)
=sin(3π/4-a)+cos(5π/4-a)
=√2/2*cosa-√2/2*sina-√2/2cosa-√2/2*sina
=-√2sina
k是偶数
k=2n
则原式=sin(kπ-π/4-a)+cos(kπ+π/4-a)
=sin(-π/4-a)+cos(π/4-a)
=-√2/2*cosa-√2/2*sina+√2/2cosa+√2/2*sina
=0
k=2n-1
则原式=sin(kπ-π/4-a)+cos(kπ+π/4-a)
=sin(3π/4-a)+cos(5π/4-a)
=√2/2*cosa-√2/2*sina-√2/2cosa-√2/2*sina
=-√2sina
k是偶数
k=2n
则原式=sin(kπ-π/4-a)+cos(kπ+π/4-a)
=sin(-π/4-a)+cos(π/4-a)
=-√2/2*cosa-√2/2*sina+√2/2cosa+√2/2*sina
=0
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