Y = (SiNx + cosx) ^ 2 + 2cosx ^ 2, find the decreasing interval, maximum and minimum

Y = (SiNx + cosx) ^ 2 + 2cosx ^ 2, find the decreasing interval, maximum and minimum

Simplification
Y = 1 + sin2x + cos2x + 1 = radical 2 * sin (2x + π / 4) + 2
The decreasing interval is [- 3 π / 8 + K π, π / 8 + K π] (K ∈ z)
The maximum value is 2 + radical 2
The minimum value is 2-radical 2

Find the maximum and minimum of y = SiNx + 2, y = 2-1 / 2cosx, y = SiNx + cosx

Y = SiNx + 2, because - 1 ≤ SiNx ≤ 1, so: the maximum value of Y is 2 + 1 = 3Y, the minimum value of y = 2-1 = 1y = 2-1 / 2cosx, because - 1 ≤ cosx ≤ 1, so: - 1 / 2 ≤ - 1 / 2cosx ≤ 1 / 2, so: the maximum value of y = 2 + 1 / 2 = 2 and 1 / 2Y, the minimum value of y = 2-1 / 2 = 1 and 1 / 2Y = SiNx + cosx = √ 2Sin (x + π / 4)