Consider the equation .

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

Problem

Consider the equation sin⁡3x  cos⁡2x  (tan⁡x−1)=0\sin 3x\;\cos 2x\;(\tan x-1)=0. (i) Obtain the general solution of sin⁡3x=0\sin 3x = 0. (ii) Obtain the general solution of cos⁡2x=0\cos 2x = 0. (iii) Solve tan⁡x−1=0\tan x - 1 = 0 for its general solution. (iv) Combine the results of (i)–(iii) to write the complete general solution of the given equation. (v) Determine all solutions in the interval [0,2π)[0,2\pi) and state their total count.

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