Solve the differential equation: `tany dx+tanx dy=0`

Explanation

To solve the differential equation \( \tan y \, dx + \tan x \, dy = 0 \), we can follow these steps:

### Step 1: Rearranging the Equation
We start with the given equation:
\[ \tan y \, dx + \tan x \, dy = 0 \]
We can rearrange this to isolate \( dx \) and \( dy \):
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