If `cos ^(-1) .(x)/(a)+ cos ^(-1). (y)/(b) = theta` then prove that
`(x^(2))/(a^(2)) -(2xy)/(ab) . cos theta+ (y^(2))/(b^(2)) = sin ^(2) theta`.

Explanation

To prove the equation given the condition \( \cos^{-1} \left( \frac{x}{a} \right) + \cos^{-1} \left( \frac{y}{b} \right) = \theta \), we will follow these steps:

### Step 1: Use the identity for the sum of inverse cosines
We start with the identity:
\[ \cos^{-1}(u) + \cos^{-1}(v) = \cos^{-1}(uv - \sqrt{(1-u^2)(1-v^2)}) \]
Let \( u = \frac{x}{a} \) and \( v = \frac{y}{b} \). Then we can write:
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