What is the general solution for sin(x)-sin^2(x)= 1/4 ?

The general solution for sin(x)-sin^2(x)= 1/4 is x= pi/6+2pin,x=(5pi)/6+2pin

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sin(x)-sin^2(x)= 1/4

sin (x) - sin^{2} (x) = \frac{1}{4}

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

Solution steps

sin (x) - sin^{2} (x) = \frac{1}{4}

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

20 sin (x) = 20 cos (x)

\frac{- 5 cot ( x )}{2} + \frac{7}{3} = - \frac{1}{6}

8.59 tan^{2} (θ) - 24 tan (θ) + 15.29 = 0

(csc (x)) = - csc (x) cot (x)

cot (x) = - \frac{4}{3}

What is the general solution for sin(x)-sin^2(x)= 1/4 ?
The general solution for sin(x)-sin^2(x)= 1/4 is x= pi/6+2pin,x=(5pi)/6+2pin