If `x=a sin theta` and `y=b cos theta`, then prove `: (x^(2))/(a^(2))+(y^(2))/(b^(2))=1`

Explanation

To prove that \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) given \(x = a \sin \theta\) and \(y = b \cos \theta\), we can follow these steps:

### Step 1: Express \(\sin \theta\) and \(\cos \theta\) in terms of \(x\) and \(y\)

From the given equations:
- \(x = a \sin \theta\) implies \(\sin \theta = \frac{x}{a}\)
- \(y = b \cos \theta\) implies \(\cos \theta = \frac{y}{b}\)

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