SiNx + cosx = √ 2m, find the value range of M

SiNx + cosx = √ 2m, find the value range of M

sinx+cosx=√2(√2/2*sinx+√2/2*cosx)
=√2(cos45°*sinx+sin45°*cosx)
=√2sin(x+45°)
So - √ 2 ≤ √ 2Sin (x + 45 °) ≤ √ 2
So - √ 2 ≤ SiNx + cosx ≤ √ 2
That is - √ 2 ≤ √ 2m ≤ √ 2
-1≤m≤1