What is the general solution for 8sin(θ)+1=6sin(θ) ?

The general solution for 8sin(θ)+1=6sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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8sin(θ)+1=6sin(θ)

8 sin (θ) + 1 = 6 sin (θ)

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

8 sin (θ) + 1 = 6 sin (θ)

Solve by substitution

sin (θ) = - \frac{1}{2}

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

- cot^{2} (x) = 1 + 2 cot (x)

6 sec (2 x) + 3 tan (2 x) - 9 = 0

3 cos^{2} (x) + 3 = 4, 0 \leq x < 2 π

tan (2 x) = 3

3 = tan (x)

What is the general solution for 8sin(θ)+1=6sin(θ) ?
The general solution for 8sin(θ)+1=6sin(θ) is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin