If `sin^(-1)(5/x)+sin^(-1)((12)/x)=pi/2,` then `x` is equal to `7/(13)` (b) `4/3` (c) `13` (d) `(13)/7`

Explanation

To solve the equation \( \sin^{-1}\left(\frac{5}{x}\right) + \sin^{-1}\left(\frac{12}{x}\right) = \frac{\pi}{2} \), we can follow these steps:

### Step 1: Set Up the Equation
Let:
\[ a = \sin^{-1}\left(\frac{5}{x}\right) \quad \text{and} \quad b = \sin^{-1}\left(\frac{12}{x}\right) \]
From the given equation, we have:
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