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

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

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

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

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

Solution steps

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

Solve by substitution

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

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

sin (x) = - 2 :

No Solution

Combine all the solutions

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

tan (x) sec (x) + 3 tan (x) = 0

\frac{csc ( b )}{csc ( b )} = \frac{1}{1 - sin ^{2} ( b )}

3 sec (4 x) = 2

2 cos (x) - 1 = cos (2 x)

0 = 4 cos (2 θ)

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