# Let's do some calculus! (30)

**Calculus**Level 3

\[\large \lim_{x \to 0} \frac{\ln \left[\cot \left( \frac \pi 4 - k_1 x \right)\right]}{\tan \left(k_2 x\right)} = 1\]

If real numbers \(k_1\) and \(k_2\) satisfy the equation above. Find the value of \(\dfrac {k_2} {k_1}\).

**Notation:** \(\ln (\cdot)\) denotes the natural logarithm function, that is \(\log_{e}{(\cdot)}\).