If sin A = 1/2, A is an acute angle, then find the value of (tan A- cot A)/(sqrt3(1+ cosecA))

If sin A = 1/2, A is an acute angle, then find the value…

If sin A = 1/2, A is an acute angle, then find the value of $\frac{tan A- cot A}{\sqrt3(1+ cosecA)}$

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Correct answer: C

Explanation

The correct answer is Option 3 i.e $-\frac{2}{9}$ .

⇒ sin A = 1/2

⇒ sin A = sIn 30°

⇒ A = 30°

Now, $\frac{tan A- cot A}{\sqrt3(1+ cosecA)}$ = $\frac{tan \ 30 °- cot\ 30 °}{\sqrt3(1+ cosec \ 30 °)}$

⇒ $\frac{\frac{1}{\sqrt3}- \sqrt3}{\sqrt3(1+ 2)}$

⇒ $-\frac{2}{9}$