y=sinx^2+sin2x+3cos^2x

= 1-cos^2x+sin2x+3cos^2x

= 1+2cos^2x+sin2x

= 1+ 1+cos2x+sin2x

=2+√2sin(2x+π/4)

X=Kπ+5π/8, when y is minimum, k ∈ z.

When x∈[Kπ-3π/8, Kπ+π/8], the function monotonically increases.

When x∈[Kπ+π/8, Kπ+5π/8], the function monotonically decreases.

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