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

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

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sin(θ)+sin(3θ)=0

sin (θ) + sin (3 θ) = 0

θ = πn, θ = \frac{π}{2} + πn

Solution steps

sin (θ) + sin (3 θ) = 0

Rewrite using trig identities

2 cos (θ) sin (2 θ) = 0

Solving each part separately

cos (θ) = 0 or sin (2 θ) = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

sin (2 θ) = 0 : θ = πn, θ = \frac{π}{2} + πn

Combine all the solutions

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

Merge Overlapping Intervals

θ = πn, θ = \frac{π}{2} + πn

4 sin^{2} (x) - 1 = 0, 0 \leq x < 2 π

cos^{2} (x) - 4 sin^{2} (x) = 2

sin (x) = 0.53

2 cos (2 θ) = 2

2 + sin (x) = 0

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