What is the general solution for sin(4x)cos(x)-cos(4x)sin(x)=0 ?

The general solution for sin(4x)cos(x)-cos(4x)sin(x)=0 is x=(2pin)/3 ,x= pi/3+(2pin)/3

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sin(4x)cos(x)-cos(4x)sin(x)=0

sin (4 x) cos (x) - cos (4 x) sin (x) = 0

x = \frac{2 πn}{3}, x = \frac{π}{3} + \frac{2 πn}{3}

Solution steps

sin (4 x) cos (x) - cos (4 x) sin (x) = 0

Rewrite using trig identities

sin (4 x - x) = 0

General solutions for

sin (4 x - x) = 0

4 x - x = 0 + 2 πn, 4 x - x = π + 2 πn

Solve

4 x - x = 0 + 2 πn : x = \frac{2 πn}{3}

Solve

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

x = \frac{2 πn}{3}, x = \frac{π}{3} + \frac{2 πn}{3}

2 sin (x) - (2 - 2) = 2 csc (x)

5 sin (62.83 x) = - 0.32

6 cos^{2} (θ) - 5 = 6 sin^{2} (θ) + sin (θ)

sin (\frac{1}{3} x) = 0

2 sec^{2} (x) - 2 sec (x) = 4

What is the general solution for sin(4x)cos(x)-cos(4x)sin(x)=0 ?
The general solution for sin(4x)cos(x)-cos(4x)sin(x)=0 is x=(2pin)/3 ,x= pi/3+(2pin)/3