Simplify (2sin45 - tan45)/(4tan60) and leave your answer in the form of (sqrt(a)-sqrt(b))/c

To answer this question we need to remember the exact trig values.A trick I use for remembering these is the hand rule.For this you label any one of your hands with the set angles starting at your pinky finger (smallest angle for the smallest finger). So the little finger is 0 degrees, ring is 30 degrees, middle is 45 degrees and so on for 60 and 90 degrees. For the angle you want to find you need to place this finger down and follow the hand rule. For sine you need you need to remember the rule of square rooting the number of fingers underneath and then dividing by 2 (will become clear when doing example). And for cosine the rule is square rooting the number of fingers above and dividing by two. For tan, put the finger down, flip your hand round and the do the square root of fingers above divided by square root of fingers below.Therefore for sin45 we get sqrt(2)/2, tan45 we get sqrt(2)/sqrt(2), which simplifies to 1, tan60 we get sqrt(3)/sqrt(1), which simplifies to sqrt(3).So on the numerator (the top of the fraction) we get 2*(sqrt(2)/2))-1, where the 2s cancel out to give sqrt(2)-1.On the denominator (bottom of fraction) we get 4sqrt(3).Next we have to rationalise this fraction, meaning that there isnt any sqrts on the bottom of the fraction, to get it into the form the question asks for.As there is a 4sqrt(3) on the bottom we are going to times by sqrt(3) as sqrt(3)sqrt(3)=3. Therefore the bottom becomes 43=12.What we do to the bottom of the fraction we also have to do to the top, therefore we have to times the top by sqrt(3) also. THis becomes sqrt(3)(sqrt(2)-1)= sqrt(6)-sqrt(3)We now have it in the form required so the answer is (sqrt(6)-sqrt(3))/12 where a=6, b=3, c=12