sinα+cosα=1 则sin2011α=cos2011α=______

问题描述:

sinα+cosα=1 则sin2011α=cos2011α=______
就这样
是cos2011α+sin2011α=_______

sinα+cosα=1,
cos(a-π/4)=1/√2,
∴a-π/4=2kπ土π/4,
∴a=(2k+1/2)π,或2kπ,k∈Z,
cos2011α+sin2011α=-1或1.