Question : The value of $(\operatorname{cosec}A+\cot A)(1 - \cos A)$ is:
Option 1: $\cos A$
Option 2: $\tan A$
Option 3: $\cot A$
Option 4: $\sin A$
Correct Answer: $\sin A$
Solution :
$(\operatorname{cosec}A+\cot A)(1 - \cos A)$
$=\left(\frac{1}{\sin A} + \frac{\cos A}{\sin A}\right)(1 - \cos A)$
$=\left(\frac{1 + \cos A}{\sin A}\right)(1 - \cos A)$
$=\frac{1 - \cos^2 A}{\sin A}$
$=\frac{\sin^2 A}{\sin A}$ [We know that $1 - \cos^2 A = \sin^2 A$]
$=\sin A$
Hence, the correct answer is $\sin A$.
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