已知函数f(X)=sinxcosx+cosx的平方,求f(X)的值域
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f(x)=sinxcosx+cos^2 x
=1/2sin2x+1/2cos2x-1/2
=√2/2(sin2x*√2/2+cos2x*√2/2)-1/2
=√2/2sin(2x+π/4)-1/2
因为-1<=sin(2x+π/4)<=1
所以-√2/2<=√2/2sin(2x+π/4)<=√2/2
-√2/2-1/2<=√2/2sin(2x+π/4)-1/2<=√2/2-1/2
所以f(x)的值域是[-√2/2-1/2，√2/2-1/2]
=1/2sin2x+1/2cos2x-1/2
=√2/2(sin2x*√2/2+cos2x*√2/2)-1/2
=√2/2sin(2x+π/4)-1/2
因为-1<=sin(2x+π/4)<=1
所以-√2/2<=√2/2sin(2x+π/4)<=√2/2
-√2/2-1/2<=√2/2sin(2x+π/4)-1/2<=√2/2-1/2
所以f(x)的值域是[-√2/2-1/2，√2/2-1/2]
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