f(x) = kx – Sin x
f’(x) = k – Cos x
For, f(x) to be increasing, it must have
f’(x) > 0
\(\therefore\) k – Cos x > 0
k > Cos x
Cos x < k
\(\because\) the minimum value of Cos x is 1.
Also, Cos x < k
\(\therefore\) The minimum value of k is 1.
\(\therefore\) k ∈ (1, ∞)
Hence the required set of values is k ∈ (1, ∞).