What is the general solution for 4sin(θ)=sin(2θ) ?

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

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4sin(θ)=sin(2θ)

4 sin (θ) = sin (2 θ)

θ = 2 πn, θ = π + 2 πn

Solution steps

4 sin (θ) = sin (2 θ)

Subtract

sin (2 θ)

from both sides

4 sin (θ) - sin (2 θ) = 0

Rewrite using trig identities

4 sin (θ) - 2 cos (θ) sin (θ) = 0

Factor

4 sin (θ) - 2 cos (θ) sin (θ) : - 2 sin (θ) (cos (θ) - 2)

- 2 sin (θ) (cos (θ) - 2) = 0

Solving each part separately

sin (θ) = 0 or cos (θ) - 2 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

cos (θ) - 2 = 0 :

No Solution

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

2 sin (3 x + \frac{3 π}{2}) = 1

n = (2 tan^{3} (2 θ) - 1)^{\frac{1}{2}}

0 = 2 sin (x + 1) + 1

tan (θ) \cdot 10 = 10

4 cos (x) + tan (4 5^{\circ}) = 0.6

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