If cos (theta) = (frac{sqrt{3}}{2}) and (theta) is less than 90o. Calculate (frac{cot(90 – theta)}{sin^2theta})

A.
(frac{4}{sqrt{3}}) 
B.
(4 sqrt{3}) 
C.
(sqrt{frac{3}{2}}) 
D.
(frac{1}{sqrt{3}}) 
E.
(frac{2}{sqrt{3}})
Correct Answer: Option B
Explanation
(frac{cot (90 – theta)}{sin^2theta})
(cot (90 – theta) = tan theta)
(therefore frac{cot (90 – theta)}{sin^{2} theta} = frac{tan theta}{sin^{2} theta})
(tan theta = sqrt{3})
(sin theta = frac{1}{2} implies sin^{2} theta = frac{1}{4})
(frac{cot(90 – theta)}{sin^{2} theta} = frac{sqrt{3}}{frac{1}{4}})
= (4 sqrt{3})