Prove that: `tan^-1(1/4)+tan^-1(2/9)=1/2 cos^-1(3/5)`.

Explanation

To prove that \( \tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) = \frac{1}{2} \cos^{-1}\left(\frac{3}{5}\right) \), we will start by using the formula for the sum of inverse tangents.

### Step 1: Apply the formula for the sum of inverse tangents
We know that:
\[ \tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\frac{a + b}{1 - ab}\right) \]
for \( ab < 1 \).
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