已知tanx=根号2,求2cos2(x/2)-sinx-1/sinx+cosx的值

已知tanx=根号2
则[2cos2(x/2)-sinx-1]/(sinx+cosx)
=(cosx-sinx)/(sinx+cosx)
=(1-tanx)/(tanx+1)
=(1-√2)/(1+√2)
=(1-√2)²/[(1+√2)(1-√2)]
=(3-2√2)/(1-2)
=2√2-3