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

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

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sin(x)=1-2sin^2(x)

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

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Solve by substitution

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

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

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

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 sin^{2} (t) - cos (t) - 1 = 0

4 cos^{2} (θ) = 1, 0 \leq θ < 2 π

cos (\frac{x}{2} + \frac{π}{3}) = \frac{2}{2}

tan (θ) = 8.2

2 sin (x) = 4 sin (x) + 1

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