Solve the equations.`tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,(x >0)`

Explanation

To solve the equation \( \tan^{-1}\left(\frac{1-x}{1+x}\right) = \frac{1}{2}\tan^{-1}(x) \) for \( x > 0 \), we can follow these steps:

### Step 1: Use the tangent addition formula
We know that:
\[ \tan^{-1}(a) - \tan^{-1}(b) = \tan^{-1}\left(\frac{a - b}{1 + ab}\right) \]
We can rewrite the left-hand side of the equation using this formula. Let \( a = \frac{1-x}{1+x} \) and \( b = 0 \):
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