A-LevelMathematicsTrigonometry9709/33 · Oct/Nov 2019 · Q47 Marks
By first expanding tan(2x + x), show that the equation tan 3x = 3 cot x can be written in the form tan⁴x - 12 tan²x + 3 = 0.
- (i)By first expanding tan(2x + x), show that the equation tan 3x = 3 cot x can be written in the form tan⁴x - 12 tan²x + 3 = 0.[4]
- (ii)Hence solve the equation tan 3x = 3 cot x for 0° < x < 90°.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [M1] Use tan (A + B) formula to express the LHS in terms of tan 2x and tan x
- [M1] Using the tan 2A formula, express the entire equation in terms of tan x
- [A1] Obtain a correct equation in tan x in any form
- [A1] Obtain the given form correctly
- [M1] Use correct method to solve the given equation for x
- [A1] Obtain answer, e.g. x = 26.8°
- [A1] Obtain second answer, e.g. x = 73.7° and no other
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