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

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

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

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

x = πn, x = \frac{π}{2} + πn

Solution steps

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

sin (x) = \frac{8}{12}

2 cos (θ) sin (θ) + 3 cos (θ) = 0

2 - 2 sin (θ) = 4

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

tan^{2} (x) sin (x) - \frac{sin ( x )}{3} = 0

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