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

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

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

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

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

Solution steps

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

sec (\frac{π}{3})

arctan (1)

tan (\frac{3 π}{2})

cos (- \frac{7 π}{4})

cot (\frac{5 π}{6})

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