Question

Evaluate the following:

`cot^2 30^circ - 2cos^2 30^circ - 3/4 sec^2 45^circ + 1/4 "cosec"^2 30^circ`

Answer 1

On substituting the values of various T-ratios, we get:

`cot^2 30^circ-2cos^2 30^circ-3/4 sec^2 45^circ +1/4 cosec^2 30^circ`

=`(sqrt(3))^2 - 2 xx(sqrt(3)/2)^2 - 3/4 xx(sqrt(2))^2+1/4xx(2)^2`

=`3-2xx3/4-3/4xx2+1/4xx4`

=`3-3/2-3/2+1`

=`4-(3/2+3/2)`

`=4-3=1`