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

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

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4sin(θ)=4-4sin(θ)

4 sin (θ) = 4 - 4 sin (θ)

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

Solution steps

4 sin (θ) = 4 - 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

tan (θ) = (- 3)

sin^{2} (x) + cos (x) + 1 = 0, 0 \leq x \leq 2 π

sin (2 x) = \frac{- 1}{3}

cos (2 θ) = 1 + 3 sin (θ)

cos (2 x) - cos (x) = - 1, 0 \leq x < 2 π

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