# Why does something like this happen to the derivative?

$$\Rightarrow (\sec^2 \theta) \frac{d \theta}{dt} = \frac{A \frac{dB}{dt} - B \frac{dA}{dt}}{A^2}$$ $$\Rightarrow \frac{d \theta}{dt} = (\cos^2 \theta) \left(\frac{A \frac{dB}{dt} - B \frac{dA}{dt}}{A^2} \right)$$

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?

-
Because $\sec(\theta) = \frac{1}{\cos(\theta)}$ by definition. –  Sasha Nov 18 '11 at 16:42

By definition $\sec \theta = \frac{1}{\cos \theta}$, so it disappears from the left-hand side when you multiply by the cosine.