If `x=a\ s e c^3theta` and `y=a\ t a n^3theta` , find `(dy)/(dx)` at `theta=pi/3`

Explanation

To find \(\frac{dy}{dx}\) given \(x = a \sec^3 \theta\) and \(y = a \tan^3 \theta\), we can follow these steps:

### Step 1: Differentiate \(x\) with respect to \(\theta\)
Given:
\[ x = a \sec^3 \theta \]
Using the chain rule, we differentiate:
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