Simplify (2sin45 - tan45) / 4tan60

Here we are dealing with 2 concepts: trigonometry and surds.First i would make sure that the student is aware/can identify these trigonometry values.So sin45 = 1/√ 2, tan45 = 1, tan60 = √ 3Now i would insert those values into the equation making it become: (2(1/√2)-1)/4√3Now, i would explain the rules behind the simplification of surds and how to rationalise a demonator. First I would rationalise sin45 = 1/√2 = √2/2. So the fraction now is (2(√2/2)-1)/4√3, which can be simplified to (√2 - 1)/4√3.Now i would rationalise the demonator by multiplying the fraction by √3/√3, so the equation becomes (√3)(√2 - 1)/(4√3)(√3). This can now be written as (√6 - √3)/12.