What is the general solution for 2sin^2(x)+(sqrt(3)-4)sin(x)=2sqrt(3) ?

The general solution for 2sin^2(x)+(sqrt(3)-4)sin(x)=2sqrt(3) is x=(4pi)/3+2pin,x=(5pi)/3+2pin

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2sin^2(x)+(sqrt(3)-4)sin(x)=2sqrt(3)

2 sin^{2} (x) + (3 - 4) sin (x) = 23

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

2 sin^{2} (x) + (3 - 4) sin (x) = 23

Solve by substitution

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

sin (x) = 2 :

No Solution

sin (x) = - \frac{3}{2} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

4 cos (30 x) + 12 = 10.5

3 sin^{2} (x) + 5 cos (x) = 1

1 + 4 sin (θ) = 0

2 sin (x) + cos (x) = - 2

sin (x) - sin (2 x) = 0, x \leq 2 π, 0

What is the general solution for 2sin^2(x)+(sqrt(3)-4)sin(x)=2sqrt(3) ?
The general solution for 2sin^2(x)+(sqrt(3)-4)sin(x)=2sqrt(3) is x=(4pi)/3+2pin,x=(5pi)/3+2pin