化简f(x)=(1-√2*cos(2x-π/4))/sin(π/2-x)

化简f(x)=(1-√2*cos(2x-π/4))/sin(π/2-x)
化简f(x)=(1-√2*cos(2x-π/4))/sin(π/2-x)

化简f(x)=(1-√2*cos(2x-π/4))/sin(π/2-x)
先看分子
1-√2*cos(2x-π/4)
=1-√2[cos2xcos(π/4)+sin2xcos(π/4)]
=1-cos2x-sin2x
=2sin²x-2sinxcosx
=2sinx(sinx-cosx)
分母=cosx
原式=2tanx(sinx-cosx)