If f (x) = (1 - λ) SiNx - (1 / 2 + 1 / 2 λ) cosx + 1 is an increasing function in [- π / 2, π / 2], find the range of λ!

If f (x) = (1 - λ) SiNx - (1 / 2 + 1 / 2 λ) cosx + 1 is an increasing function in [- π / 2, π / 2], find the range of λ!

If f (x) = (1 - λ) SiNx - (1 / 2 + 1 / 2 λ) cosx + 1 is an increasing function in [- π / 2, π / 2], find the range of λ!
Analysis: let cos θ = (1 - λ) / √ [5 / 4 + 5 λ ^ 2 / 4-3 λ / 2], sin θ = (1 / 2 + 1 / 2 λ) / √ [5 / 4 + 5 λ ^ 2 / 4-3 λ / 2]
∴f(x)=√[5/4+5λ^2/4-3λ/2]sin(x-θ)+1
For f (x) to be an increasing function in [- π / 2, π / 2], we must make θ = 0
Let 1 / 2 + 1 / 2 λ = 0 = = > λ = - 1
If f (x) is an increasing function in [- π / 2, π / 2], λ = - 1