1.求f(x)=sin(x-π/4)cos(x+π/4)的反函数 原函数定义域为π/4

题目

1.求f(x)=sin(x-π/4)cos(x+π/4)的反函数 原函数定义域为π/4

答案

1.y=f(x)=-cos(x-π/4+π/2)cos(x+π/4)
=-[cos(x+π/4)]^2
=-[1+cos(2x+π/2)]/2
=(sin2x-1)/2
x=(1/2)arc sin(2y+1) y∈[-1/2,0]
2.y= arcsin(cos4) -arccos(sin5)
siny=sin[arcsin(cos4)]cos[arccos(sin5)]-cos[arcsin(cos4)]
sin[arccos(sin5)]
=cos4sin5-sin4cos5
=sin(5-4)
=sin1
y=1
3.y=arctanx
tany=x
x