g(x)=根号2sin(2x+pai/4+a),0

[2cos^2(a/2)-sina-1]/根号2sin(π/4+a)
=(cosa-sina)/[√2（√2/2sina+√2/2cosa)] (2cos²a/2-1=cosa, sin(π/4+a)展开）
=(cosa-sina)/(cosa+sina)
=(1-tana)/(1+tana) （分子分母同时除以coaa)
=(1-2)/(1+2)
=-1/3

根号2sin(π/3-x)+根号6cos(π/3-x)
=2√2*[sin(π/3-x)(1/2)+(√3/2)cos(π/3-x)]
=2√2*[sin(π/3-x)*cos(π/3)+cos(π/3-x)*sin(π/3)]
=2√2*sin[(π/3-x)+π/3]
=2√2*sin(2π/3-x)

最后是π/8吧
2sinπ/32*cosπ/32*cosπ/16*cosπ/8
=sinπ/16*cosπ/16*cosπ/8
=(1/2)sinπ/8cosπ/8
=(1/4)sinπ/4
=(√2)/8

f(x)=|sinx+cosx|
=|√2（√2/2*sinx+√2/2*cosx|
=|√2（sinx*cosπ/4+cosx*sinπ/4）|
=|√2sin(x+π/4)|.

联立方程
x+y=根号2sin(α+π/4)
x-y=根号2sin(α-π/4)
解得：x=(根号2/2)*(sin(α+π/4)+sin(α-π/4)),y=(根号2/2)*(sin(α+π/4)-sin(α-π/4))；
由三角和差化积公式得：sin(α+π/4)=sinα*cos(π/4)+cosα*sin(π/4),sin(α-π/4)=sinα*cos(π/4)-cosα*sin(π/4)；
故sin(α+π/4)+sin(α-π/4)=2*sinα*cos(π/4)=根号2*sinα；
sin(α+π/4)-sin(α-π/4)=2*cosα*sin(π/4)=根号2*cosα；
代入x,y可得：x=sinα,y=cosα；
所以,x²+y²=sin²α+cos²α=1.

2x=√2（sin(a+π/4)+sin(a-π/4))=√2(sin(a+π/4)-cos(a+π/4))
2y=√2(sin(a+π/4)+cos(a+π/4))
x^2+y^2=1/2(sin(a+π/4)-cos(a+π/4))^2+1/2(sin(a+π/4)+cos(a+π/4))^2
=1/2(1-sin2a)+1/2(1+sin2a)=1

2x=√2（sin(a+π/4)+sin(a-π/4))=√2(sin(a+π/4)-cos(a+π/4))
2y=√2(sin(a+π/4)+cos(a+π/4))
x^2+y^2=1/2(sin(a+π/4)-cos(a+π/4))^2+1/2(sin(a+π/4)+cos(a+π/4))^2
=1/2(1-sin2a)+1/2(1+sin2a)=1