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

The general solution for sin^2(x)+2sin(x)+1=0 is x=(3pi)/2+2pin

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sin^2(x)+2sin(x)+1=0

sin^{2} (x) + 2 sin (x) + 1 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (x) + 2 sin (x) + 1 = 0

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

4 cos^{2} (x) = 2

sin (x) = - \frac{1}{5}

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

sin (x) = \frac{4}{7}

sin^{2} (θ) - cos^{2} (θ) = cos (θ) + 1

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