Question #18059
solve x: sin (x+30) = - 2 cos x
Expert's answer
Notice that
sin(x+30) =sin(x)*cos(30) - cos(x)*sin(30)
=sqrt(3)/2 * sin(x) - 1/2 * cos(x).
Thus
sqrt(3)/2 * sin(x) - 1/2 * cos(x) = - 2 cos(x)
sqrt(3)/2 * sin(x) = -3/2 * cos(x)
sin(x)/cos(x) = -sqrt(3)
tan(x) = -sqrt(3)
x = - 60 + 180 * k, k belongs to Z
sin(x+30) =sin(x)*cos(30) - cos(x)*sin(30)
=sqrt(3)/2 * sin(x) - 1/2 * cos(x).
Thus
sqrt(3)/2 * sin(x) - 1/2 * cos(x) = - 2 cos(x)
sqrt(3)/2 * sin(x) = -3/2 * cos(x)
sin(x)/cos(x) = -sqrt(3)
tan(x) = -sqrt(3)
x = - 60 + 180 * k, k belongs to Z
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