If \( \sin A=\frac{\sqrt{3}}{2} \) and \( A \) is an acute angle, t...

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If \( \sin A=\frac{\sqrt{3}}{2} \) and \( A \) is an acute angle, then find the value of \( \frac{\tan A-\cot A}{\sqrt{3}+\operatorname{cosec} A} \).
(a) \( \frac{-2}{5} \)
(b) \( \frac{2}{5} \)
(c) \( \frac{2}{3+2 \sqrt{3}} \)
(d) \( -2 \)
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