求y=sin(x-π/4)cos(x+π/4)的反函数 (1)x属于【-π/4,π/4】 (2)x属于【π/4,π/2】急啊,求详解

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求y=sin(x-π/4)cos(x+π/4)的反函数 (1)x属于【-π/4,π/4】 (2)x属于【π/4,π/2】急啊,求详解

求y=sin(x-π/4)cos(x+π/4)的反函数 (1)x属于【-π/4,π/4】 (2)x属于【π/4,π/2】急啊,求详解
求y=sin(x-π/4)cos(x+π/4)的反函数 (1)x属于【-π/4,π/4】 (2)x属于【π/4,π/2】
急啊,求详解

求y=sin(x-π/4)cos(x+π/4)的反函数 (1)x属于【-π/4,π/4】 (2)x属于【π/4,π/2】急啊,求详解
y=sin(x-pi/4)sin(pi/2-(x+pi/4))
=sin(x-pi/4)sin(pi/4-x)
=-(sin(x-pi/4))^2
=(cos2x-1)/2
=cos2x/2-1/2
1)反余弦值域是[0,pi],x属于【-π/4,π/4】
2x...[-pi/2,pi/2]
2x=arccos(1+2y)+pi/2.[0,pi]
x=1/2arccos(1+2y)+pi/4
2) x属于【π/4,π/2】
2x.[pi/2,pi]
2x=arccos(1+2y)
x=1/2arccos(1+2y)