Find the principal and general solutions of the equation`sqrt2 sin x+1=0`

Explanation

To solve the equation \( \sqrt{2} \sin x + 1 = 0 \) and find both the principal and general solutions, we can follow these steps:

### Step 1: Simplify the Equation
Start with the given equation:
\[ \sqrt{2} \sin x + 1 = 0 \]
Subtract 1 from both sides:
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