Question

Evaluate:

`(5 cos^2 60^circ + 4 sec^2 30^circ - tan^2 45^circ)/(sin^2 30^circ + cos^2 30^circ)`

Answer 1

`(5 cos^2 60^circ + 4 sec^2 30^circ - tan^2 45^circ)/(sin^2 30^circ + cos^2 30^circ)`

=`(5(1/2)^2+4(2/sqrt(3))^2-(1)^2)/((1/2)^2+(sqrt(3)/2)^2)`

=`((5/4 + (4xx4)/3-1))/((1/4+3/4)`

=`((5/4+16/3-1))/((4/4))`

=`(((15  +  64  -  12)/12))/((4/4))`

=`((67/12))/((1))`

=`67/12`