Question #6eeed

1 Answer
Nghi N
Jun 9, 2017

#x = (kpi)/2#
#x = kpi#

Explanation:

Transpose all terms to the left side:
sin 3x + sin x - 2sin 2x = 0 (1)
Use trig identity:
#sin a + sin b = 2sin ((a + b)/2)cos ((a - b)/2)#
In this case:
sin 3x + sin x = 2sin (2x).cos x
The equation (1) becomes:
#2sin (2x).cos x - 2sin (2x) = 0#
#[2sin (2x)](cos x - 1) = 0#
Either factor must be zero.
a. cos x = 1 --> x = 0, and #x = 2pi#
General answers: #x = 2kpi#
b. sin 2x = 0
2x = 0 --> #2x = pi#, --> #2x = 2pi# -->
x = 0, --> #x = pi/2#, --> #x = pi#.
General answers: #x = (kpi)/2#

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