Let's do some calculus! (30)

Calculus Level 4

limx0ln[cot(π4k1x)]tan(k2x)=1\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 k1k_1 and k2k_2 satisfy the equation above. Find the value of k2k1\dfrac {k_2} {k_1}.

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

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