化简 sin(4k-1/4π- α)+cos(4k+1/4π -α)(k∈Z)

问题描述:

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=-√2sinak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...