Express a trigonometrical expression as an integral polynomial in $\alpha$ & $\beta$ How could we express this ![enter image description here]( as an integral polynomial in $\alpha$& $\beta$ ? I tried a lot but cannot get any start .

HINT:

If $\tan^{-1}u=A;\tan A=u,\cos A=+\dfrac1{\sqrt{1+u^2}}$

$\csc^2\dfrac A2=\dfrac2{1-\cos A}$

If $\tan^{-1}v=B;\tan B=v,\cos B=+\dfrac1{\sqrt{1+v^2}}$

$\sec^2\dfrac B2=\dfrac2{1+\cos B}$

Formula used: $\cos2y=1-2\sin^2y=2\cos^2y-1$