If `sin (sin^(-1).(1)/(5) + cos^(-1) x) = 1`, then find the value of x

Explanation

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

### Step 1: Understand the condition for sine
The sine function equals 1 at specific angles. The primary angle where \( \sin(\theta) = 1 \) is \( \theta = \frac{\pi}{2} \). Therefore, we can set the argument of the sine function equal to \( \frac{\pi}{2} \):

\[ \sin^{-1}\left(\frac{1}{5}\right) + \cos^{-1}(x) = \frac{\pi}{2} \]
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