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 \(\log_{e}{(\cdot)}\).


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