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

The general solution for -2sin^2(x)=-3sin(x)+1 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin

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-2sin^2(x)=-3sin(x)+1

- 2 sin^{2} (x) = - 3 sin (x) + 1

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

Solution steps

- 2 sin^{2} (x) = - 3 sin (x) + 1

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

sin (x) = \frac{6}{10}

sin (3 x) = 3 cos (3 x)

(9 sin (2 x) + 9 cos (2 x))^{2} = 81

- 2 cos^{2} (θ) + sin (θ) - 3 = - 4

sec^{2} (x) - 9 sec (x) = 0

What is the general solution for -2sin^2(x)=-3sin(x)+1 ?
The general solution for -2sin^2(x)=-3sin(x)+1 is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin