Question

函数y=sin平方x-cosx,x∈{-π|4,π|4}的值域为

Answer 1

y=(sinx)^2-cosx
=1-(cosx)^2-cosx
=-(cosx+1/2)^2+5/4
x∈(-π/4,π/4)
cosx∈(√2/2,1)
令cosx=1,得y=-1
令cosx=√2/2,得y=(1-√2)/2
函数的值域为((1-√2)/2,1)