What is the general solution for sin(3θ)cos(θ)-cos(3θ)sin(θ)=(sqrt(3))/2 ?

The general solution for sin(3θ)cos(θ)-cos(3θ)sin(θ)=(sqrt(3))/2 is θ= pi/6+pin,θ= pi/3+pin

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sin(3θ)cos(θ)-cos(3θ)sin(θ)=(sqrt(3))/2

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

θ = \frac{π}{6} + πn, θ = \frac{π}{3} + πn

Solution steps

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

Rewrite using trig identities

sin (3 θ - θ) = \frac{3}{2}

General solutions for

sin (3 θ - θ) = \frac{3}{2}

3 θ - θ = \frac{π}{3} + 2 πn, 3 θ - θ = \frac{2 π}{3} + 2 πn

Solve

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

Solve

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

θ = \frac{π}{6} + πn, θ = \frac{π}{3} + πn

tan (x) = 3 cot (x)

2 cos (\frac{1}{2} x) - 1 = 0

2 cos (θ) sin (θ) - sin (θ) = 0

2 sin (x) cot (x) - cot (x) = - 1 + 2 sin (x)

sin (3 θ) = cos (3 θ)

What is the general solution for sin(3θ)cos(θ)-cos(3θ)sin(θ)=(sqrt(3))/2 ?
The general solution for sin(3θ)cos(θ)-cos(3θ)sin(θ)=(sqrt(3))/2 is θ= pi/6+pin,θ= pi/3+pin