Quantitative Aptitude Trigonometry Trigonometric Ratios and Identities

If \(sin A=\frac{1}{2}\), A is an acute angle, then find the value of \(\frac{tan A-cot A}{\sqrt 3(1+cosecA)}\).

1
\(\frac{4\sqrt3}{9}\)
2
\(-\frac{4\sqrt3}{9}\)
3
\(-\frac{2}{9}\)
4
\(\frac{2}{9}\)

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