What is the general solution for sin(3x)cos(x)=-cos(3x)sin(x) ?

The general solution for sin(3x)cos(x)=-cos(3x)sin(x) is x=(pin)/2 ,x= pi/4+(pin)/2

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sin(3x)cos(x)=-cos(3x)sin(x)

sin (3 x) cos (x) = - cos (3 x) sin (x)

x = \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}

Solution steps

sin (3 x) cos (x) = - cos (3 x) sin (x)

Subtract

- cos (3 x) sin (x)

from both sides

sin (3 x) cos (x) + cos (3 x) sin (x) = 0

Rewrite using trig identities

sin (3 x + x) = 0

General solutions for

sin (3 x + x) = 0

3 x + x = 0 + 2 πn, 3 x + x = π + 2 πn

Solve

3 x + x = 0 + 2 πn : x = \frac{πn}{2}

Solve

3 x + x = π + 2 πn : x = \frac{π}{4} + \frac{πn}{2}

x = \frac{πn}{2}, x = \frac{π}{4} + \frac{πn}{2}

6 sin^{2} (x) + sin (x) - 1 = 0

sin (2 x) - 2 cos^{2} (x) = 0

sin^{2} (x) - 7 cos (x) + 7 = 0

sin (x) - 3 = - sin (x)

6 sin (θ) - 6 = 0

What is the general solution for sin(3x)cos(x)=-cos(3x)sin(x) ?
The general solution for sin(3x)cos(x)=-cos(3x)sin(x) is x=(pin)/2 ,x= pi/4+(pin)/2