Question #6eeed

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Question #6eeed

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Answer 1 · 2017-06-09T17:01:00

$x = \frac{k π}{2}$ $x = (kpi)/2$
$x = k π$ $x = kpi$

Explanation:

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

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Question #6eeed

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