作业帮求值域：f(x)=(1+根号3倍tanx)cosx,x属于[0,π\2]
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![求值域：f(x)=(1+根号3倍tanx)cosx,x属于[0,π\2]](/uploads/image/z/3777716-20-6.jpg?t=%E6%B1%82%E5%80%BC%E5%9F%9F%EF%BC%9Af%28x%29%3D%281%2B%E6%A0%B9%E5%8F%B73%E5%80%8Dtanx%29cosx%2Cx%E5%B1%9E%E4%BA%8E%5B0%2C%CF%80%5C2%5D)
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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]