Answer to Question #18059 in Trigonometry for Marica

Question

solve x: sin (x+30) = - 2 cos x

Answer 1

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