How do you find all solutions of the equation $sin(3x)cosx-sinx cos(3x)=0$ ?

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Answer 1 · 2015-05-05T03:02:27

Trig identity: $sin (a - b) = sin a.cos b - sin b.cos a$

$f(x) = sin (3x - x) = sin 2x = 0 -> 2x = 0; and 2x = 2Pi; and 2x = Pi$

$2x = 0 -> x = 0$

$2x = 2Pi -> x = Pi$

$2x = Pi -> x = Pi/2$

How do you find all solutions of the equation sin(3x)cosx-sinx cos(3x)=0sin(3x)cosx-sinx cos(3x)=0?