If `sin^(-1)(x/5)+cose c^(-1)(5/4)=pi/2` then the value of x is: (1) 1 (2) 3 (3) 4 (4) 5

Explanation

To solve the equation \( \sin^{-1}\left(\frac{x}{5}\right) + \cos^{-1}\left(\frac{5}{4}\right) = \frac{\pi}{2} \), we can follow these steps:

### Step 1: Use the identity for inverse trigonometric functions
We know that:
\[ \cos^{-1}(y) = \frac{\pi}{2} - \sin^{-1}(y) \]
Thus, we can rewrite \( \cos^{-1}\left(\frac{5}{4}\right) \) as:
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