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 + (4 xx 4)/3 - 1))/((1/4 + 3/4)`

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

= `(((15  +  64  -  12)/12))/((4/4))`

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

= `67/12`