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