Prove that: `(alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^2)/2sec^2(1/2tan^(-1)beta/alpha)=(alpha+beta)(a^2+beta^2)dot`

Explanation

To prove the equation

\[ \frac{\alpha^3}{2 \cos^2\left(\frac{1}{2} \tan^{-1}\left(\frac{\alpha}{\beta}\right)\right)} + \frac{\beta^3}{2 \sec^2\left(\frac{1}{2} \tan^{-1}\left(\frac{\beta}{\alpha}\right)\right)} = (\alpha + \beta)(\alpha^2 + \beta^2) \]

we will start by simplifying the left-hand side (LHS) and show that it equals the right-hand side (RHS).

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