Solve the equation .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve the equation

\tan 3x = \tan x

. (i) Show that the given equation can be rewritten in the equivalent form

\sin 2x\,\cos x = 0

. (ii) Hence find every solution in the interval

0 < x < 2\pi

. (iii) Deduce the general solution for all real

x