Solve equation: (Is my answer correct ?)

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1 Answer
Jun 27, 2018

x = kpi; x = pi/2 + kpi
x = pi/6 + (kpi)/3

Explanation:

sin^2 2x = sin^2 3x - sin^2 x(1)
Develop the right side:
RS = (sin 3x - sin x)(sin 3x + sin x)
RS = (2cos 2x.sin x)(2sin 2x.cos x) = (2sin x.cos x)(2sin 2x.cos 2x)=
RS = sin 2x.sin 4x
Equation (1) becomes:
sin^2 2x = sin 2x.sin 4x sin^2 2x - sin 2x sin 4x = 0
sin 2x(sin 2x - sin 4x) = 0
Either factor should be zero.

a. sin 2x = 0. Unit circle gives:
2x = 2kpi --> x = kpi
2x = pi + 2kpi --> x= pi/2 + kpi

b. sin 4x = sin 2x
Unit circle gives:
4x = 2x + 2kpi, and 4x = pi - 2x + 2kpi
1. 4x = 2x + 2kpi --> 2x = 2kpi --> x = kpi
2. 4x = pi - 2x + 2kpi --> 6x = pi + 2kpi
x = (pi)/6 + (kpi)/3