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High school mathematics compound trigonometric function to find monotone increasing interval … Come on, master! ?
Expand the brackets, merge the square of sin+the square of +cos, and get the double root of y=sin2x+cos2x+2= sin(2x+π/4)+2 by the double angle formula.
The monotonic increasing range is (-3π/8+2kπ, π/8+2kπ).