O-LevelAdditional MathematicsTrigonometry4037/11 · May/June 2016 · Q97 Marks
Show that 2cosx cotx + 1 = cotx + 2cosx can be written in the form (a cosx - b)(cosx - sinx) = 0, where a and b are constants to be found.
- (i)Show that 2cosx cotx + 1 = cotx + 2cosx can be written in the form (a cosx - b)(cosx - sinx) = 0, where a and b are constants to be found.[4]
- (ii)Hence, or otherwise, solve 2cosx cotx + 1 = cotx + 2cosx for 0 < x < π.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [1] 2 cos x (cos x / sin x) + 1 = (cos x / sin x) + 2 cos x
- [1] 2 cos²x + sin x = cos x + 2 cos x sin x
- [1] 2 cos²x - 2 cos x sin x = cos x - sin x
- [1] (2 cos x - 1)(cos x - sin x) = 0
- [1] 2 cos x - 1 = 0 or cos x - sin x = 0
- [1] cos x = 1/2
- [1] tan x = 1
- [1] x = π/3, x = π/4
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