TMUA 2019 Paper 2 Q6 — Worked Solution

P2·Trigonometry, Logic & Quantifiers·6.5Official · 2019 · Q6

proof-errortrig-equationinvalid-implication

A student attempts to solve the equation

cos x + sin x tan x = 2 sin x - 1

in the range

0 \leq x \leq 2 π

. The student's attempt is as follows.

(I)

cos x - sin x + sin x tan x - sin x = - 1

(II)

(sin x - cos x) (tan x - 1) = - 1

(III)

sin x - cos x = - 1

tan x - 1 = - 1

(IV)

(sin x - cos x)^{2} = 1

tan x = 0

(V)

2 sin x cos x = 0

tan x = 0

(VI)

x = 0, \frac{π}{2}, π, \frac{3 π}{2}, 2 π

Which of the following best describes this attempt?

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