JEE Math Practice Question

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

1. A.$$15{x^2} - 8x - 7 = 0$$
2. B.$$5{x^2} - 12x + 7 = 0$$
3. C.$$25{x^2} - 18x - 7 = 0$$
4. D.$$25{x^2} - 32x + 7 = 0$$