# Answer to Question #18059 in Trigonometry for Marica

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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