f(x) = kx – Sin x

f’(x) = k – Cos x

For, f(x) to be increasing, it must have

f’(x) > 0

k – Cos x > 0

k > Cos x

Cos x < k

the minimum value of Xos x is 1.

Also, Cos x < k

The minimum value of k is 1.

k ϵ (1, ∞)

Hence the required set of values is k ϵ (1, ∞).