What is the general solution for 4sin(θ)-sqrt(3)=2sin(θ) ?

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

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4sin(θ)-sqrt(3)=2sin(θ)

4 sin (θ) - 3 = 2 sin (θ)

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

Solution steps

4 sin (θ) - 3 = 2 sin (θ)

Solve by substitution

sin (θ) = \frac{3}{2}

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

Combine all the solutions

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

cos (2 x) = - 0.5

5 cos (x) - 5 sin (x) = 0

32 + 6 sin (x) = 0

5 tan (θ) = 4

3 sec (θ) + 5 = - 1

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