求值域：f(x)=(1+根号3倍tanx)cosx,x属于[0,π\2]

求值域：f(x)=(1+根号3倍tanx)cosx,x属于[0,π\2]
求值域：f(x)=(1+根号3倍tanx)cosx,x属于[0,π\2]

求值域：f(x)=(1+根号3倍tanx)cosx,x属于[0,π\2]
f(x)=(1+根号3倍tanx)cosx=cosx+根号3倍sinx
=2*(根号3/2*sinx+0.5cosx)
因为sinπ/6=0.5,cosπ/6=根号3/2
所以f(x)=2*(sinxcosπ/6+cosxsinπ/6)
=2*sin(x+π/6)
因为x∈[0,π/2] ,所以x+π/6∈[π/6,2/3π]
所以sin(x+π/6)∈[0.5,1],所以f(x)∈[1,2]