Question

Evaluate each of the following

$\frac{{\tan }^{2}60°+4{\cos }^{2}45°+3{\sec }^{2}30°+5{\cos }^{2}90°}{\mathrm{cosec}30°+\sec 60°-{\cot }^{2}30°}$

Answer 1

We have,

…… (1)

Now,

, , , , ,

So by substituting above values in equation (1)

We get,

Now,

3 gets cancel in numerator and we get,

Now, in the numerator get reduced to 2and we get,

Therefore,