(|sinx| + |cosx|)^2 = (sinx)^2 + (cosx)^2 + 2|sinxcosx| = 1 + |sin(2x)|
记t = |sin(2x)|
f(x) = √(1 + |sin(2x)|) + (sin2x)^4
=√(1 + t) + t^4
0 ≤ t ≤ 1
所以1 ≤ f(x) ≤ 1+√2
当x = kπ + π/4时取得最大值1+√2
当x = kπ/2时取得最小值1
k是整数