If \[\mathbf{2 sin }\alpha \mathbf{=}\sqrt{\mathbf{3}}\] then \[\frac{\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\alpha \mathbf{+3}\mathbf{.cot}\alpha }{\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}\alpha \mathbf{+2tan}\alpha }\] is equal to ______ (where \[\alpha \] is an acute angle)

\[\frac{3(\sqrt{3}+1)}{1+6\sqrt{3}}\]

\[\frac{-\,45-51\sqrt{3}}{-107}\]

If \[\mathbf{2 sin }\alpha \mathbf{=}\sqrt{\mathbf{3}}\] then \[\frac{

1.	If \[\mathbf{2 sin }\alpha \mathbf{=}\sqrt{\mathbf{3}}\] then \[\frac{\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\alpha \mathbf{+3}\mathbf{.cot}\alpha }{\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}\alpha \mathbf{+2tan}\alpha }\] is equal to ______ (where \[\alpha \] is an acute angle)
A.	\[\frac{3(\sqrt{3}+1)}{1+6\sqrt{3}}\]
B.	\[\frac{-\,45-51\sqrt{3}}{-107}\]
C.	\[\frac{50\sqrt{3}+45}{-106}\]
D.	\[\frac{-\,51\sqrt{3}}{107}\]
E.	None of these
Answer» C. \[\frac{50\sqrt{3}+45}{-106}\]

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If \[\mathbf{2 sin }\alpha \mathbf{=}\sqrt{\mathbf{3}}\] then \[\frac{\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\alpha \mathbf{+3}\mathbf{.cot}\alpha }{\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}\alpha \mathbf{+2tan}\alpha }\] is equal to ______ (where \[\alpha \] is an acute angle)

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