What is the general solution for sin(3x)cos(x)+cos(3x)sin(x)=1 ?

The general solution for sin(3x)cos(x)+cos(3x)sin(x)=1 is x= pi/8+(pin)/2

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sin(3x)cos(x)+cos(3x)sin(x)=1

sin (3 x) cos (x) + cos (3 x) sin (x) = 1

x = \frac{π}{8} + \frac{πn}{2}

Solution steps

sin (3 x) cos (x) + cos (3 x) sin (x) = 1

Rewrite using trig identities

sin (3 x + x) = 1

General solutions for

sin (3 x + x) = 1

3 x + x = \frac{π}{2} + 2 πn

Solve

3 x + x = \frac{π}{2} + 2 πn : x = \frac{π}{8} + \frac{πn}{2}

x = \frac{π}{8} + \frac{πn}{2}

2 sin (x) cos (x) + 2 sin (x) - cos (x) - 1 = 0

sin (θ) tan^{2} (θ) - sin (θ) = 0

sin (x) = \frac{4}{5}, sin (18 0^{\circ} - x)

- 11 cos (x) (22) - 11 sin (x) (8) = - 250

3 cos (x) + 1 = 2 sin (x)

What is the general solution for sin(3x)cos(x)+cos(3x)sin(x)=1 ?
The general solution for sin(3x)cos(x)+cos(3x)sin(x)=1 is x= pi/8+(pin)/2