What is the general solution for 4sin^2(x)+8sin(x)+4=0 ?

The general solution for 4sin^2(x)+8sin(x)+4=0 is x=(3pi)/2+2pin

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4sin^2(x)+8sin(x)+4=0

4 sin^{2} (x) + 8 sin (x) + 4 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

4 sin^{2} (x) + 8 sin (x) + 4 = 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

- 4 cos (θ) + 3 = 3

sin (2 x - 8) = sin (x - 4)

0 = 3 cos (x) + sin (x)

- 4 cos (2 θ) - 1 = - 2 cos (θ)

cos^{3} (x) = 1

What is the general solution for 4sin^2(x)+8sin(x)+4=0 ?
The general solution for 4sin^2(x)+8sin(x)+4=0 is x=(3pi)/2+2pin