Question

Evaluate:

`(sin^2 30^0 + 4 cot^2 45^0-sec^2 60^0)(cosec^2  45^0 sec^2 30^0)`

Answer 1

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

`(sin^2 30^0 + 4 cot^2 45^0-sec^2 60^0)(cosec^2  45^0 sec^2 30^0)`

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

=`(1/4+4-4)(2xx4/3)`

=`1/4xx8/3=2/3`