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

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

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

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

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

Solution steps

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

sin (2 θ) = 2 cos^{2} (θ)

0 = 3 cos (3 θ)

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

tan (2 x - \frac{π}{4}) = - 1

2 sin^{2} (A) = 5 sin (A) - 2

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