What is the general solution for 2sin^2(x)-5sin(x)=-2 ?

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

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2sin^2(x)-5sin(x)=-2

2 sin^{2} (x) - 5 sin (x) = - 2

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

Solution steps

2 sin^{2} (x) - 5 sin (x) = - 2

Solve by substitution

sin (x) = 2, sin (x) = \frac{1}{2}

sin (x) = 2 :

No Solution

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

8 sin^{2} (x) + 6 sin (x) + 1 = 0

sin (\frac{θ}{2}) = 0

tan (\frac{θ}{2} - \frac{π}{4}) = 1

cos^{2} (x) - 3 cos (x) + 2 = 0

3 tan (x) = 3

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