What is the general solution for 8sin^2(x)+16sin(x)+8=0 ?

The general solution for 8sin^2(x)+16sin(x)+8=0 is x=(3pi)/2+2pin

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8sin^2(x)+16sin(x)+8=0

8 sin^{2} (x) + 16 sin (x) + 8 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

8 sin^{2} (x) + 16 sin (x) + 8 = 0

Solve by substitution

sin (x) = - 1

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

tan (θ) = \frac{2 3}{3} sin (θ), 0 \leq θ < 2 π

3 tan (x) = cot (x)

cos (θ) = \frac{7}{25}

2 tan^{2} (θ) sin (θ) - tan^{2} (θ) = 0

sin^{2} (x) = - 3 sin (x) + 4

What is the general solution for 8sin^2(x)+16sin(x)+8=0 ?
The general solution for 8sin^2(x)+16sin(x)+8=0 is x=(3pi)/2+2pin