Question 56

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:

Solution

$$\frac{\tan 30^\circ \cosec 60^\circ + \tan 60^\circ \sec 30^\circ}{\sin^2 30^\circ + 4 \cot^2 45^\circ - \sec^2 60^\circ}$$

On put the values,

= $$\frac{\frac{1}{\sqrt3} \times \frac{2}{\sqrt3} + \sqrt3 \times \frac{2}{\sqrt3}}{(\frac{1}{2})^2 + 4 \times 1 - 2^2}$$

= $$\frac{\frac{2}{3} + 2}{\frac{1}{4} + 4 - 4}$$

= $$\frac{\frac{8}{3}}{\frac{1}{4}}$$

= $$\frac{32}{3}$$

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