The value of $$\frac{(\sin \theta - \cos \theta)(1 + \tan \theta + \cot \theta)}{1 + \sin \theta \cos \theta} = ?$$

$$\frac{(\sin \theta - \cos \theta)(1 + \tan \theta + \cot \theta)}{1 + \sin \theta \cos \theta}$$
Let the $$\theta$$ be $$45\degree$$,
= $$\frac{(\sin 45\degree- \cos 45\degree)(1 + \tan 45\degree + \cot 45\degree)}{1 + \sin 45\degree \cos 45\degree}$$
=  $$\frac{(\frac{1}{\sqrt{2}}- \frac{1}{\sqrt{2}})(1 + 1 + 1)}{1 + \frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}}}$$
= $$\frac{(0)(1 + 1 + 1)}{1 + \frac{1}{\sqrt{2}} \frac{1}{\sqrt{2}}}$$ = 0
From the option A,
$$\sec \theta - \cosec \theta$$
On put the $$\theta$$ = $$45\degree$$,
= $$\sec 45\degree - \cosec 45\degree$$
= \sqrt{2} - \sqrt{2} = 0