(cosec- )^2=? - Vidyadip

MCQ

$(\operatorname{cosec}-\cot \theta)^2=?$

A
$\frac{1+\cos \theta}{1-\cos \theta}$
✓
$\frac{1-\cos \theta}{1+\cos \theta}$
C
$\frac{1+\sin \theta}{1-\sin \theta}$
D
None of these

✓

Answer

Correct option: B.

$\frac{1-\cos \theta}{1+\cos \theta}$

$(\operatorname{cosec} \theta-\cot \theta)^2$
$=\left(\frac{1}{\sin \theta}-\frac{\cos \theta}{\sin \theta}\right)^2$
$=\frac{(1-\cos \theta)^2}{\sin ^2 \theta}=\frac{(1-\cos \theta)^2}{1-\cos ^2 \theta}$
$=\frac{(1-\cos \theta)^2}{(1-\cos \theta)(1+\cos \theta)}$
$=\frac{1-\cos \theta}{1+\cos \theta}$

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