The value of(1 + cot θ - cosec θ) (1 + tan θ + sec θ) is equal to

$$(1 + cot θ - cosec θ) = (1+\frac{cos θ}{sinθ} - \frac{1}{sinθ})$$
$$= \frac{sin \theta + cos \theta -1}{sinθ}$$
$$(1 + tanθ + sec θ) = (1+\frac{sin θ}{cosθ} - \frac{1}{cosθ})$$
$$= \frac{sin \theta + cos \theta +1}{cosθ}$$
$$(1 + cot θ - cosec θ) (1 + tan θ + sec θ) = ( \frac{sin \theta + cos \theta -1}{sinθ})( \frac{sin \theta + cos \theta +1}{cosθ})$$
$$ ( \frac{sin \theta + cos \theta -1}{sinθ})( \frac{sin \theta + cos \theta +1}{cosθ}) = \frac{(sin \theta + cos \theta)^2 -1}{2}$$
$$= \frac{(sin \theta + cos \theta)^2 -1}{sin \theta cos \theta} = \frac{sin ^2 \theta + cos^2 \theta + 2 sin \theta cos\theta -1}{sin \theta cos \theta} = 2$$
Option B is the correct answer.