Good evening Sonia! Here are my workings for this question.

Parts a and b are very similar, where we express 15 and 75 as 45 - 30 and 45 + 30 and then use the addition angle formula to simplify the expression. We need to know the special angle values as well.

Part c is quadratic factorisation a2 - b2 = (a + b) (a - b).

Part d uses the complementary angle rule, cos x = sin (90 - x).

Part e is simplification from parts c and d.

Let me know if you need more explanation and I will do my best to explain them again!