Prove the following: `tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)(a/b)]=(2b)/a`

Explanation

To prove the equation

\[ \tan\left(\frac{\pi}{4} + \frac{1}{2}\cos^{-1}\left(\frac{a}{b}\right)\right) + \tan\left(\frac{\pi}{4} - \frac{1}{2}\cos^{-1}\left(\frac{a}{b}\right)\right) = \frac{2b}{a} \]

we will use the tangent addition and subtraction formulas.

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