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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Solve by substitution

sin (x) = - 1

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

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

cos (2 x) = 11 sin (x) - 5

x, z = \frac{4}{π} arctan (x y)

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

x, cos (2 x) + sin (x) = 0

sin (x) = \frac{- 1}{3}

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