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Official 2019 Paper 2 · Q6

Paper 2TrigonometryFunctions & graphsAlgebra

A student attempts to solve the equation

cos⁡x+sin⁡xtan⁡x=2sin⁡x−1\cos x+\sin x\tan x=2\sin x-1

in the range 0≤x≤2π0\leq x\leq2\pi.

The student's attempt is as follows:

cos⁡x+sin⁡xtan⁡x=2sin⁡x−1\cos x+\sin x\tan x=2\sin x-1
  • (I) So cos⁡x−sin⁡x+sin⁡xtan⁡x−sin⁡x=−1\cos x-\sin x+\sin x\tan x-\sin x=-1
  • (II) So (sin⁡x−cos⁡x)(tan⁡x−1)=−1(\sin x-\cos x)(\tan x-1)=-1
  • (III) So sin⁡x−cos⁡x=−1\sin x-\cos x=-1 or tan⁡x−1=−1\tan x-1=-1
  • (IV) So (sin⁡x−cos⁡x)2=1(\sin x-\cos x)^2=1 or tan⁡x=0\tan x=0
  • (V) So 2sin⁡xcos⁡x=02\sin x\cos x=0 or tan⁡x=0\tan x=0
  • (VI) So x=0,π2,π,3π2,2πx=0,\frac\pi2,\pi,\frac{3\pi}2,2\pi

Which of the following best describes this attempt?

AIt is completely correct
BIt is incorrect, and the first error occurs on line (I)
CIt is incorrect, and the first error occurs on line (II)
DIt is incorrect, and the first error occurs on line (III)
EIt is incorrect, and the first error is that extra solutions were introduced on line (IV)
FIt is incorrect, and the first error is that extra solutions were introduced on line (V)
GIt is incorrect, and the first error is not eliminating the values where tan⁡x\tan x is undefined on line (VI)

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