What is the general solution for sin^2(x)+6sin(x)=2sin(x)-3 ?

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

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sin^2(x)+6sin(x)=2sin(x)-3

sin^{2} (x) + 6 sin (x) = 2 sin (x) - 3

x = \frac{3 π}{2} + 2 πn

Solution steps

sin^{2} (x) + 6 sin (x) = 2 sin (x) - 3

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

sin (x) + cos (x) = \frac{1}{5}

cos (\frac{2 x}{3}) - 1 = 0

4 sin^{2} (θ) - 11 sin (θ) + 7 = 0

cos^{2} (x) + cos^{4} (x) = 1

- 3 cos (θ) = 2

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