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

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

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