What is the general solution for 2sin^2(w)+sin(w)-1=0 ?

The general solution for 2sin^2(w)+sin(w)-1=0 is w= pi/6+2pin,w=(5pi)/6+2pin,w=(3pi)/2+2pin

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2sin^2(w)+sin(w)-1=0

2 sin^{2} (w) + sin (w) - 1 = 0

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

Solution steps

2 sin^{2} (w) + sin (w) - 1 = 0

Solve by substitution

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

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

sin (w) = - 1 : w = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

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

arctan (x) = arccos (\frac{3}{4})

tan^{2} (θ) + 7 tan (θ) + 9 = 0

x, cos (x) \cdot cos (y) = 0

3 sec (θ) = 6

What is the general solution for 2sin^2(w)+sin(w)-1=0 ?
The general solution for 2sin^2(w)+sin(w)-1=0 is w= pi/6+2pin,w=(5pi)/6+2pin,w=(3pi)/2+2pin