If is the interior angle of a regular octagon, then _ ^ + - 1 [ +… - Vidyadip

MCQ

If $\alpha $ is the interior angle of a regular octagon, then $\mathop {\lim }\limits_{\theta \to {\alpha ^ + }} \frac{{\tan \theta - 1}}{{\left[ {\sin \theta + \cos \theta } \right]}}$ is equal to (Note : $[k]$ denotes greatest integer less than or equal to $k$ )

A
$0$
B
$-1$
C
$1$
✓
$2$

✓

Answer

Correct option: D.

$2$

d
$\alpha=135^{\circ}$

$\mathop {\lim }\limits_{\theta \to \frac{{3\pi }}{4}} \frac{{\tan \theta - 1}}{{[\sin \theta + \cos \theta ]}} = \frac{{ - 2}}{{ - 1}} = 2$

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