If $$\frac{{\cos \theta }}{{1 - \sin \theta }}$$   + $$\frac{{\cos \theta }}{{1 + {\text{sin }}\theta }}$$   = 4, then the value of $$\theta \left( {{0^ \circ } < \theta < {{90}^ \circ }} \right)$$   is?

Solution (By Examveda Team)

$$\eqalign{ & \Rightarrow \frac{{\cos \theta }}{{1 - \sin \theta }} + \frac{{\cos \theta }}{{1 + \sin \theta }} = 4 \cr & \Rightarrow \cos \theta \left( {\frac{{1 + \sin \theta + 1 - \sin \theta }}{{1 - {{\sin }^2}\theta }}} \right) = 4 \cr & \Rightarrow \cos \theta \left( {\frac{2}{{{\text{co}}{{\text{s}}^2}\theta }}} \right) = 4 \cr & \Rightarrow \cos \theta = \frac{1}{2} \cr & \Rightarrow \theta = {60^ \circ } \cr} $$