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

Explanation

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

### Step 1: Understand the condition for sine to equal 1
The sine function equals 1 at specific angles. The primary angle where this occurs is \( \frac{\pi}{2} \). Therefore, we can set up the equation:
\[ \sin(\sin^{-1} \frac{1}{5} + \cos^{-1} x) = 1 \implies \sin^{-1} \frac{1}{5} + \cos^{-1} x = \frac{\pi}{2} \]

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