What is the general solution for 5+2sin^2(x)=3sin(x)+4 ?

The general solution for 5+2sin^2(x)=3sin(x)+4 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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5+2sin^2(x)=3sin(x)+4

5 + 2 sin^{2} (x) = 3 sin (x) + 4

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

Solution steps

5 + 2 sin^{2} (x) = 3 sin (x) + 4

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 (x) + 1 = cos (x) + 1

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

sin (\frac{π}{x}) = 0

tan (x) = \frac{150}{80}

1 - 3 cos (x) = 1

What is the general solution for 5+2sin^2(x)=3sin(x)+4 ?
The general solution for 5+2sin^2(x)=3sin(x)+4 is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin