Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

Let R=$\sqrt{{\alpha }^2+{\beta }^2}$. The first half-angle has ${\sin }^2=(R-\beta )/(2R)$; the second has ${\cos }^2=(R+\alpha )/(2R)$. The sum ${\alpha }^{3}R/(R-\beta )+{\beta }^{3}R/(R+\alpha )$ simplifies to ($\alpha +\beta$)(${\alpha }^2+{\beta }^2$).