Question

Evaluate each of the following

${\cot }^{2}30°-2{\cos }^{2}60°-\frac{3}{4}{\sec }^{2}45°-4{\sec }^{2}30°$

Answer 1

We have,

…… (1)

Now,

,, ,

So by substituting above values in equation (1)

We get,

Now, in the third term 4 gets cancelled by 2 and 2 remains

Therefore,

Now in the second term, 4 gets cancelled by 2 and 2 remains

Therefore,

Now, LCM of denominator in the above expression is 6

Therefore by taking LCM

We get,

Now in the above expression, gets reduced to

Therefore,