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

The general solution for -2sin^2(x)-3sin(x)+2=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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

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

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

Solution steps

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

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

tan (β) = \frac{1}{2}

cos (B) = \frac{4}{5}

2 sin^{2} (x) - 3 cos (2 x) = 3

cos (π + x) + sin (x - \frac{π}{2}) = 1

sin^{2} (a) + \frac{1}{sec ( a )} = \frac{5}{4}

What is the general solution for -2sin^2(x)-3sin(x)+2=0 ?
The general solution for -2sin^2(x)-3sin(x)+2=0 is x= pi/6+2pin,x=(5pi)/6+2pin