What is the general solution for sin(4x)cos(x)-cos(4x)sin(x)=1 ?

The general solution for sin(4x)cos(x)-cos(4x)sin(x)=1 is x= pi/6+(2pin)/3

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sin(4x)cos(x)-cos(4x)sin(x)=1

sin (4 x) cos (x) - cos (4 x) sin (x) = 1

x = \frac{π}{6} + \frac{2 πn}{3}

Solution steps

sin (4 x) cos (x) - cos (4 x) sin (x) = 1

Rewrite using trig identities

sin (4 x - x) = 1

General solutions for

sin (4 x - x) = 1

4 x - x = \frac{π}{2} + 2 πn

Solve

4 x - x = \frac{π}{2} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{3}

x = \frac{π}{6} + \frac{2 πn}{3}

sec (θ) = \frac{10}{6}

x, 2 cos (3 x) = - 3

x, 7 - 3 cos (x) = 9 sin^{2} (x)

4 sin (x) = 3 tan (x)

sin^{2} (x) + sin (x) = 1

What is the general solution for sin(4x)cos(x)-cos(4x)sin(x)=1 ?
The general solution for sin(4x)cos(x)-cos(4x)sin(x)=1 is x= pi/6+(2pin)/3