Prove: `tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/(sqrt(5)))`

Explanation

To prove that \( \tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{2}{9}\right) = \sin^{-1}\left(\frac{1}{\sqrt{5}}\right) \), we will use the addition formula for inverse tangent functions and some trigonometric identities.

### Step 1: Use the addition formula for inverse tangent
The addition formula for inverse tangent states that:
\[ \tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\frac{a + b}{1 - ab}\right) \]
provided that \( ab < 1 \).
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