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

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

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

2 sin (x) + \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}{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

3 tan (2 x) = 3

12 cos^{2} (x) = 3

2 cos (x) - 2 sin (x) = 1, 0 \leq x < 2 π

sin (x) = 3 cos (x)

2 sin^{2} (x) - 3 cos (x) = 3

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