`(tan60^(@)-tan30^(@))/(1+tan 60^(@) tan30^(@))+cos60^(@) cos30^(@)+sin60^(@) sin 30^(@)`

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

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

`=(4+6)/(4sqrt(3))=(10)/(4sqrt(3))=(5)/(2sqrt(3))`