JEE Advance - Mathematics (1991 - No. 4)
If $$\exp \,\,\,\left\{ {\left( {\left( {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + \,\,\,..............\infty } \right)\,In\,\,2} \right)} \right\}$$ satiesfies the equation $${x^2} - 9x + 8 = 0,$$ find the value of $${{\cos x} \over {\cos x + \sin x}},\,0 < x < {\pi \over 2}.$$
$$\frac{\sqrt{3} + 1}{2}$$
$$\frac{\sqrt{3} - 1}{2}$$
$$\frac{1}{\sqrt{3} + 1}$$
$$\frac{1}{\sqrt{3} - 1}$$
$$\frac{\sqrt{2} - 1}{2}$$