已知tan2a= -2√2 π小于2a小于2π 求(2cos^2 (a/2)-sina-1)/√2sin(a+ π /4)

π <2a<2π √2 π小
π /2<a<π
tana<0
tsn2a=2tana/(1-tana^2)=-2√2
tana=-√2/2
tan(a+π/4)=(-√2/2+1)/(1-(-√2/2))
=(2-√2)/(2+√2)
原式=（cosa-sina）/(√2sin(a+π/4))
=(√2cos(a+π/4))/(√2sin(a+π/4))
=cot(a+π/4)
=(2+√2)/(2-√2)
=3+2√2

答案经过计算器验证，绝对正确。