The value of $$\frac{\tan 30^\circ \cosec 60^\circ + \tan 60^\circ \sec 30^\circ}{\sin^2 30^\circ + 4 \cot^2 45^\circ - \sec^2 60^\circ}$$ is:
$$\frac{\tan 30^\circ \cosec 60^\circ + \tan 60^\circ \sec 30^\circ}{\sin^2 30^\circ + 4 \cot^2 45^\circ - \sec^2 60^\circ}$$
On put the values,
=Â $$\frac{\frac{1}{\sqrt3} \times \frac{2}{\sqrt3}Â + \sqrt3 \times \frac{2}{\sqrt3}}{(\frac{1}{2})^2 + 4 \times 1 - 2^2}$$
= $$\frac{\frac{2}{3} + 2}{\frac{1}{4} + 4Â - 4}$$
= $$\frac{\frac{8}{3}}{\frac{1}{4}}$$
= $$\frac{32}{3}$$
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