f(x)=sinx∨6+conx∨6的值域

Question

f(x)=sinx∨6+conx∨6的值域

Answer 1

f(x)
=(sinx)^6+(cosx)^6
=[(sinx)^2+(cosx)^2]*[(sinx)^4-(sinx)^2*(cosx)^2+(cosx)^4]
=1*{[(sinx)^2+(cosx)]^2-3(sinx)^2*(cosx)^2}
=1-(3/4)sin2x
∵sin2x∈[-1,1]
∴f(x)∈[1/4,7/4].