How do you solve $sin2x+sin4x= 0$ ?

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Answer 1 · 2015-06-12T17:58:27

Solve f(x) = sin 2x + sin 4x = 0

Use the trig identity: sin a + sin b = $2sin ((a + b)/2) cos ((a -b)/2)$

f(x) = 2sin 3x.cos x = 0

Next solve sin 3x = 0 and solve cos x = 0.

a. sin 3x = 0 --> 3x = 0 and 3x = pi - 0 = pi --> $x = pi/3$

and 3x = 2pi --> $x = 2pi/3$

b. cos x = 0 --> $x = pi/2$ and $x = 3pi/2$

Answers within interval $(0, 2pi):$
$0, pi/3, pi/2, (2pi)/3, (3pi)/2 and 2pi$

How do you solve sin2x+sin4x= 0sin2x+sin4x= 0?