Solution
$$(\operatorname{cosec}A-\cot A)(1+\cos A)=\left(\frac{1}{\sin A}-\frac{\cos A}{\sin A}\right)\left(1+\cos A\right)$$
= $$\left(\frac{1-\cos A}{\sin A}\right)\left(1+\cos A\right)$$
= $$\left(\frac{1-\cos^2A}{\sin A}\right)$$
= $$\frac{\sin^2A}{\sin A}$$
= $$\sin A$$
Hence, the correct answer is Option B
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