What is the general solution for sin^2(x)+4sin(x)+3=0 ?

The general solution for sin^2(x)+4sin(x)+3=0 is x=(3pi)/2+2pin

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sin^2(x)+4sin(x)+3=0

sin^{2} (x) + 4 sin (x) + 3 = 0

x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (x) + 4 sin (x) + 3 = 0

Solve by substitution

sin (x) = - 1, sin (x) = - 3

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

sin (x) = - 3 :

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

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

4 cos (2 θ) + 3 cos (θ) + 4 = - 3 cos (θ) - 1

cos (θ - \frac{π}{4}) - 1 = 0

x, - sin (x) = 0

2 sec^{2} (x) tan (x) = 0

What is the general solution for sin^2(x)+4sin(x)+3=0 ?
The general solution for sin^2(x)+4sin(x)+3=0 is x=(3pi)/2+2pin