trig values - simplify fractions with radicals

[carebear]

The question is tan(2pi/3)cos(-5pi/4) + sin(3pi/2)tan(5pi/6) and the answer I get is (3sqrt2 +2)/2sqrt3 but the answer key says (3 +sqrt2)/sqrt6. When I check them on the calculator, they are equal values, but would both answers be acceptable provided that the question did not ask for a rational denominator?

Thanks very much for your help.

 

[tkhunny]

1) Please do not rely on answer sheets to learn. They can get you started.
2) It's a little odd to leave radicals in the denominator (although it doesn't bother me). I'm a little surprised the "right" answer is like that.
3) Learn to manipulate the symbols. Myltiply numerator and denominator by sqrt(2) and see what happens.