What is the general solution for sin(3x)cos(x)-cos(3x)sin(x)=0 ?

The general solution for sin(3x)cos(x)-cos(3x)sin(x)=0 is x=pin,x= pi/2+pin

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

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

x = πn, x = \frac{π}{2} + πn

Solution steps

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 = πn

Solve

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

x = πn, x = \frac{π}{2} + πn

4 sin (2 x) = - 2

x, sin^{2} (x) = 0

cos (t) = - \frac{3}{4}

sin (2 x) - 2 cos (x) = 2 sin (x) - 1

cos^{2} (θ) - \frac{3}{2} cos (2 θ) = 0

What is the general solution for sin(3x)cos(x)-cos(3x)sin(x)=0 ?
The general solution for sin(3x)cos(x)-cos(3x)sin(x)=0 is x=pin,x= pi/2+pin