Let α= tan ((5 π)/16 sin (2 cos^-1(1/(√ 5)))) and β= cos ( sin^-1(4/5)+ sec^-1(5/3)) where the inverse trigonometric functions take principal values.…

Let $\displaystyle \alpha=\tan \left(\frac{5 \pi}{16} \sin \left(2 \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)\right)$ and $$\beta=\cos \left(\sin ^{-1}\left(\frac{4}{5}\right)+\sec ^{-1}\left(\frac{5}{3}\right)\right) $$ where the inverse trigonometric functions take principal values. Then, the equation whose roots are $\displaystyle \alpha$ and $\displaystyle \beta$ is :