Mathematics

Problem

Consider the equation

\sin 3x\;\cos 2x\;(\tan x-1)=0

. a. (i) Obtain the general solution of

\sin 3x = 0

. b. (ii) Obtain the general solution of

\cos 2x = 0

. c. (iii) Solve

\tan x - 1 = 0

for its general solution. d. (iv) Combine the results of (i)–(iii) to write the complete general solution of the given equation. e. (v) Determine all solutions in the interval

[0,2\pi)

and state their total count.

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