已知tanα=3/4,则【1-根号2sin（2α-π/4)】/cos^2α=_数学解答

已知tanα=3/4,则【1-根号2sin（2α-π/4)】/cos^2α=

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解答

tanα=3/4
[1-√2sin(2a-π/4)]/cos²a
=[1-(sin2a-cos2a)]/cos²a
=[2cos²a-2sinacosa]/cos²a
=2-2sina/cosa
=2-2tana
=2-2*(3/4)
=1/2