If $\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$ then $x^2 - 44x - 36 = 0$ holds for $x=\sin 2A$ If 
$$\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$$
then prove that 
$$\sin 2A \quad\text{ is a root of }\quad x^2 - 44x - 36 = 0$$
I have no idea how to solve it. Plz help.

Let $$\sin{A}+\cos{A}=t$$
$$7=\sin A+\cos A+\frac{1}{\sin A\cos A}+\frac{\sin A+\cos A} {\sin A\cos A}$$
$$\sin 2A =2 \sin A \cos A$$
$$t^2=1+\sin 2A$$
