你想说的公式是asinx+bcosx=√(a²+b²)sin(x+φ) 其中sinφ=b/a,
cosx+sinx+1
=√2sin(x+π/4)+1
-1≤sin(x+π/4)≤1
1-√2≤√2sin(x+π/4)+1≤√2+1
函数的值域为[1-√2,√2+1]
2kπ-π/2≤x+π/4≤2kπ+π/2 (k∈Z)时,即2kπ-3π/4≤x≤2kπ+π/4 (k∈Z),函数单调递增.
2kπ+π/2≤x+π/4≤2kπ+3π/2 (k∈Z)时,即2kπ+π/4≤x≤2kπ+5π/4 (k∈Z),函数单调递减.