What is the general solution for sin(x)-sqrt(1-3sin^2(x))=0 ?

The general solution for sin(x)-sqrt(1-3sin^2(x))=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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sin(x)-sqrt(1-3sin^2(x))=0

sin (x) - 1 - 3 sin^{2} (x) = 0

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

sin (x) - 1 - 3 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{1}{2}

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 cos^{2} (x) + 2 cos (x) - 3 = 0

sec^{2} (x) cot (x) = 8, 0 < x < π

tan (x) = \frac{1.5}{2}

3 csc^{2} (x) - 5 csc (x) = 2

tan (2 x) - 3 tan (x) = 0

What is the general solution for sin(x)-sqrt(1-3sin^2(x))=0 ?
The general solution for sin(x)-sqrt(1-3sin^2(x))=0 is x= pi/6+2pin,x=(5pi)/6+2pin