By first expanding sin(2x + x), show that sin 3x = 3 sin x – 4 sin³ x.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [B1] (i) State correct expansion of sin(2x + x)
2. [M1] (i) Use trig formulae and Pythagoras to express sin 3x in terms of sin x
3. [A1] (i) Obtain a correct expression in any form e.g. 2sinx(1-sin²x)+sinx(1-2sin²x)
4. [AG] (i) Obtain sin 3x = 3sinx - 4 sin³ x correctly
5. [B1] (ii) Use identity, integrate and obtain -3/4 cos x + 1/12 cos 3x
6. [B1] (ii) One mark for each term correct
7. [M1] (ii) Use limits correctly in an integral of the form a cos x + b cos 3x, where ab ≠ 0
8. [A1] (ii) Obtain answer 5/24