What is the general solution for 2sin^2(x)+sqrt(3)sin(x)=0 ?

The general solution for 2sin^2(x)+sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin

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2sin^2(x)+sqrt(3)sin(x)=0

2 sin^{2} (x) + 3 sin (x) = 0

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

Solution steps

2 sin^{2} (x) + 3 sin (x) = 0

Solve by substitution

sin (x) = 0, sin (x) = - \frac{3}{2}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

cos^{2} (x) - sin (x) = 1

sec^{2} (x) - 5 tan (x) = - 3

cos (\frac{x}{2}) = cos (x)

sin (x + \frac{π}{4}) = \frac{3}{2}

2 sin (2 x) = - 3

What is the general solution for 2sin^2(x)+sqrt(3)sin(x)=0 ?
The general solution for 2sin^2(x)+sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin