A-LevelMathematicsTrigonometry9709/31 · May/June 2021 · Q36 Marks
Given that cos(x – 30°) = 2 sin(x + 30°), show that tan x = (2-√3) / (1-2√3)
- (a)Given that cos(x – 30°) = 2 sin(x + 30°), show that tan x = (2-√3) / (1-2√3)[4]
- (b)Hence solve the equation cos(x -30°) = 2 sin(x + 30°), for 0° < x < 360°.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [*M1] Use correct trig expansions and obtain an equation in sin x and cos x
- [B1 FT] Use correct exact trig ratios for 30° in their expansion
- [DM1] Obtain an equation in tan x
- [A1 AG] Obtain tan x = (2-√3) / (1-2√3) from correct working
- [B1] Obtain answer in the given interval, e.g.173.8°
- [B1] Obtain a second answer and no other in the given interval, e.g. 353.8°
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