Question

f(x)=2sinx(sinx+cosx)，x∈[-π/2，π/2]时，求f(x)的值域

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Answer 1

f(x)=2sin^2x+2sinxcosx
=1-cos2x+sin2x
=√2sin(2x-45°）+1

x∈[-π/2，π/2]
2x∈[-π，π]
2x-45∈[-5π/4，3π/4]
sin(2x-45)∈[-1,1]
f(x)∈[1-√2,1+√2]