1+ ^2 1+ e c = - Vidyadip

MCQ

$1+\frac{\cot ^2 \alpha}{1+\cos e c \alpha}=$

A
$\sin \alpha$
B
$\sec \alpha$
✓
$\operatorname{cosec} \alpha$
D
$\tan \alpha$

✓

Answer

Correct option: C.

$\operatorname{cosec} \alpha$

$\operatorname{cosec} \alpha$
$\text { Explanation: } 1+\frac{\cot ^2 \alpha}{1+\operatorname{cosec} \alpha}$
$=1+\frac{\operatorname{cosece}^2 \alpha-1}{1+\cos e c \alpha}$
$=1+\frac{(\operatorname{csec} \alpha-1)(\operatorname{cosec} \alpha+1)}{1+\operatorname{cosec} \alpha}$
$=1+\operatorname{cosec} \alpha-1$
$=\operatorname{cosec} \alpha$

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