What is the general solution for 6sin(θ)-1=4sin(θ) ?

The general solution for 6sin(θ)-1=4sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin

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6sin(θ)-1=4sin(θ)

6 sin (θ) - 1 = 4 sin (θ)

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

Solution steps

6 sin (θ) - 1 = 4 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

cot^{3} (x) = cot^{3} (x) sin (x)

3 (1 - cos (x)) = sin^{2} (x)

2 cos^{2} (θ) + 5 cos (θ) - 2 = - 4

tan (x) = \frac{2}{4}

7 cos (x) + 12 = 6 cos (x) + 13

What is the general solution for 6sin(θ)-1=4sin(θ) ?
The general solution for 6sin(θ)-1=4sin(θ) is θ= pi/6+2pin,θ=(5pi)/6+2pin