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

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

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

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

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

Solution steps

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

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

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

sin (θ) = \frac{3}{8}

sin (x) = \frac{1}{3}

2 sin^{2} (x) + 9 cos (x) = 6

3 sin (x) + cos (x) = 0

tan^{2} (x) - sec^{2} (x) = 1

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