What is the general solution for sin(6x)cos(x)=-cos(6x)sin(x) ?

The general solution for sin(6x)cos(x)=-cos(6x)sin(x) is x=(2pin)/7 ,x= pi/7+(2pin)/7

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sin(6x)cos(x)=-cos(6x)sin(x)

sin (6 x) cos (x) = - cos (6 x) sin (x)

x = \frac{2 πn}{7}, x = \frac{π}{7} + \frac{2 πn}{7}

Solution steps

sin (6 x) cos (x) = - cos (6 x) sin (x)

Subtract

- cos (6 x) sin (x)

from both sides

sin (6 x) cos (x) + cos (6 x) sin (x) = 0

Rewrite using trig identities

sin (6 x + x) = 0

General solutions for

sin (6 x + x) = 0

6 x + x = 0 + 2 πn, 6 x + x = π + 2 πn

Solve

6 x + x = 0 + 2 πn : x = \frac{2 πn}{7}

Solve

6 x + x = π + 2 πn : x = \frac{π}{7} + \frac{2 πn}{7}

x = \frac{2 πn}{7}, x = \frac{π}{7} + \frac{2 πn}{7}

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What is the general solution for sin(6x)cos(x)=-cos(6x)sin(x) ?
The general solution for sin(6x)cos(x)=-cos(6x)sin(x) is x=(2pin)/7 ,x= pi/7+(2pin)/7