Y = 1 + sin (2x) + 2cos ^ 2 (x) = 1 + sin (2x) + 1 + cos (2x) = 2 + sin (2x) + cos (2x) = 2 + √ 2Sin (2x + π / 4), so the period is π =2 + √ 2Sin (2x + π / 4)

Y = 1 + sin (2x) + 2cos ^ 2 (x) = 1 + sin (2x) + 1 + cos (2x) = 2 + sin (2x) + cos (2x) = 2 + √ 2Sin (2x + π / 4), so the period is π =2 + √ 2Sin (2x + π / 4)

Here is a formula: a * sin (x) + b * cos (x) = root sign (a ^ 2 + B ^ 2) sin (x + an angle). The angle is different according to different topics. For example, here a = 1, B = 1, root sign (a ^ 2 + B ^ 2) = √ 2, then after putting forward √ 2, it is √ 2 / 2, which is just the COS and sin value of π / 4. If a = 1, B = √ 3, then it is to extract root sign (a ^ 2 + B ^ 2) = 2, then the rest is 1 / 2, √ 3 / 2, Then the angle should be π / 3 or π / 6. This formula is widely used in trigonometric function. You can go through this content by yourself