What is the general solution for sin(θ)cos(3θ)+cos(θ)sin(3θ)=0 ?

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

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sin(θ)cos(3θ)+cos(θ)sin(3θ)=0

sin (θ) cos (3 θ) + cos (θ) sin (3 θ) = 0

θ = \frac{πn}{2}, θ = \frac{π}{4} + \frac{πn}{2}

Solution steps

sin (θ) cos (3 θ) + cos (θ) sin (3 θ) = 0

Rewrite using trig identities

sin (θ + 3 θ) = 0

General solutions for

sin (θ + 3 θ) = 0

θ + 3 θ = 0 + 2 πn, θ + 3 θ = π + 2 πn

Solve

θ + 3 θ = 0 + 2 πn : θ = \frac{πn}{2}

Solve

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

θ = \frac{πn}{2}, θ = \frac{π}{4} + \frac{πn}{2}

19 sin (x) + 9 = sin (x)

cos (x) = \frac{3}{7}

tan (\frac{x}{4}) + 3 = 0

4 sin^{2} (x) tan (x) = tan (x)

cos (- x) = - cos (x)

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