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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

Combine all the solutions

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

cos (2 x) - cos (x) + 1 = 0

4 tan^{2} (x) + 21 tan (x) - 49 = 0

cot (x) = csc (x) + 1

\frac{sin ( 8 )}{30} = \frac{sin ( x )}{120}

2 sin (2 x + 1 5^{\circ}) = 1

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