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

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

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

sin (x) + 2 sin^{2} (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{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

6 cos (x) = - 6 (1 + cos (x))

sin (θ) = \frac{60 sin ( 1 5 ^{\circ} )}{400}

sin^{2} (x) - 3 cos (x) - 1 = 0

2 cos^{2} (θ) + 2 cos (θ) = 0

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

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