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化简sin(kπ+π/3)+cos(kπ-π/6),k∈Z
题目详情
化简sin(kπ+π/3)+cos(kπ-π/6),k∈Z
▼优质解答
答案和解析
sin(kπ+π/3)+cos(kπ-π/6)=1/2sinkπ+√3/2coskπ+√3/2coskπ+1/2sinkπ
=√3coskπ+sinkπ
=2sin(kπ+π/3)
= √3,(k为偶数时)或-√3,(k为奇数时)
=√3coskπ+sinkπ
=2sin(kπ+π/3)
= √3,(k为偶数时)或-√3,(k为奇数时)
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