化简sin(4k-1/4π- α)+cos(4k+1/4π -α)(k∈Z)
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化简sin(4k-1/4π- α)+cos(4k+1/4π -α)(k∈Z)
sin(4k-1/4π- α)+cos(4k+1/4π -α)
=sin(4k-α-1/4π)+cos(4k -α+1/4π)
=sin(4k-α)cos1/4π-cos(4k-α)sin1/4π+cos(4k -α)cos1/4π-sin(4k -α)sin1/4π
因sin1/4π=cos1/4π=1/2的根号2
则原式=0
再问: 答案是对的,只是好像要分类讨论,k为奇,k为偶,答案都是0. 多谢~~
=sin(4k-α-1/4π)+cos(4k -α+1/4π)
=sin(4k-α)cos1/4π-cos(4k-α)sin1/4π+cos(4k -α)cos1/4π-sin(4k -α)sin1/4π
因sin1/4π=cos1/4π=1/2的根号2
则原式=0
再问: 答案是对的,只是好像要分类讨论,k为奇,k为偶,答案都是0. 多谢~~
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