If the equation `tan (P cot x)=cot (P tan x)` has a solution in `x in (0, pi)-{pi/2}`, then prove that `P le pi/4`.

Explanation

To prove that \( P \leq \frac{\pi}{4} \) given the equation \( \tan(P \cot x) = \cot(P \tan x) \) has a solution in \( x \in (0, \pi) - \{\frac{\pi}{2}\} \), we will follow these steps:

### Step 1: Rewrite the given equation
The original equation is:
\[ \tan(P \cot x) = \cot(P \tan x) \]
Using the identity \( \cot \theta = \tan\left(\frac{\pi}{2} - \theta\right) \), we can rewrite the right-hand side:
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