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

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

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2sin(x)+(sqrt(3))/4 = 3/2 sin(x)

2 sin (x) + \frac{3}{4} = \frac{3}{2} sin (x)

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

Solution steps

2 sin (x) + \frac{3}{4} = \frac{3}{2} sin (x)

Solve by substitution

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

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

- 2 cos^{2} (θ) + sin (θ) + 5 = 4

12 sin^{2} (x) - 9 = 0

2 cos (x - 1) = 0

5 + 6 sin (x) = 0

sin (\frac{π}{2} x) = 0

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