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

Explanation

`\frac{\alpha^{3}}{2} {cosec}^{2}(\frac{1}{2} \tan ^{-1} \frac{\alpha}{\beta})+\frac{\beta^{3}}{2} \sec ^{2}(\frac{1}{2} \tan ^{-1}(\frac{\beta}{\alpha}))`


`\frac{\alpha^{3}}{2} \frac{1}{\sin ^{2}(\frac{1}{2} \tan ^{-1} \frac{\alpha}{\beta})}+\frac{\beta^{3}}{2} \frac{1}{\cos ^{2}(\frac{1}{2} \tan ^{-1}(\frac{\beta}{\alpha}))}`



`\frac{\alpha^{3}}{1-\cos (\tan ^{-1} \frac{\alpha}{\beta})}+\frac{\beta^{3}}{1+\cos (\tan ^{-1} \frac{\beta}{\alpha})}`



...