2cosa(sina-cosa)+1=√2
2sinacosa-2cos²a+1=√2
sin2a=2sinacosa
cos2a=2cos²a-1
∴sin2a-cos2a=√2
√2（sin2acosπ/4-cos2asinπ/4）=√2
sin（2a-π/4）=1
接下去自己算吧 !