To solve the equation \( \sin x + \sin 3x + \sin 5x = 0 \), we will follow these steps:
### Step 1: Combine Sine Terms
We can group \( \sin 3x \) and \( \sin 5x \) together. We will use the sine addition formula:
\[
\sin A + \sin B = 2 \sin\left(\frac{A+B}{2}\right) \cos\left(\frac{A-B}{2}\right)
\]
Let \( A = 5x \) and \( B = 3x \):
...
