$ \Rightarrow (\sec^2 \theta) \frac{d \theta}{dt} = \frac{A \frac{dB}{dt} - B \frac{dA}{dt}}{A^2} $ $ \Rightarrow \frac{d \theta}{dt} = (\cos^2 \theta) \left(\frac{A \frac{dB}{dt} - B \frac{dA}{dt}}{A^2} \right) $
I have this. One question. I think I should divide by $\sec^2 \theta$. But I saw this solution to the problem. Why does sec become cos?