What is the general solution for 5sin(θ)-1=3sin(θ) ?

The general solution for 5sin(θ)-1=3sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin

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5sin(θ)-1=3sin(θ)

5 sin (θ) - 1 = 3 sin (θ)

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

5 sin (θ) - 1 = 3 sin (θ)

Solve by substitution

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

2 cos^{2} (w) - cos (w) - 1 = 0

3 csc (θ) - 3 = 0

2 sin (x) + (sin (x))^{2} = 0

2 cos (x) + 1 = 3, 0 \leq x \leq 2 π

1 - 2 sin (2 x) = 0

What is the general solution for 5sin(θ)-1=3sin(θ) ?
The general solution for 5sin(θ)-1=3sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin