JEE Math Practice Question

If $$\int {{{d\theta } \over {{{\cos }^2}\theta \left( {\tan 2\theta + \sec 2\theta } \right)}}} = \lambda \tan \theta + 2{\log _e}\left| {f\left( \theta \right)} \right| + C$$ where C is a constant of integration, then the ordered pair ($$\lambda $$, ƒ($$\theta $$)) is equal to :

1. A.(–1, 1 – tan$$\theta $$)
2. B.(1, 1 + tan$$\theta $$)
3. C.(–1, 1 + tan$$\theta $$)
4. D.(1, 1 – tan$$\theta $$)