Given that sin(x + π/3) – sin(x – π/3) = cos(x + π/3) – cos(x – π/3), find the exact value of tan x.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] (a) Use correct trig formulae and obtain an equation in sin x and cos x Allow one sign error.
2. [A1] (a) Obtain a correct equation in any form e.g. 2cosxsin(π/3) = -2sinx sin(π/3).
3. [DM1] (a) Substitute exact trig ratios and obtain an expression for tan x Allow one sign error.
4. [A1] (a) Obtain answer tan x = -1/√3 Or exact equivalent.
5. [B1] (b) Obtain answer, e.g. x = 5π/6
6. [B1FT] (b) Obtain second answer, e.g. x = 11π/6 and no others in the interval FT first answer + π (provided 0 < first answer ≤ π). Or FT first answer – π (provided π < first answer ≤ 2π). Ignore any answers outside interval.