What is the general solution for 2sin^2(w)-3sin(w)+1=0 ?

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

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2sin^2(w)-3sin(w)+1=0

2 sin^{2} (w) - 3 sin (w) + 1 = 0

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

Solution steps

2 sin^{2} (w) - 3 sin (w) + 1 = 0

Solve by substitution

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

sin (w) = 1 : w = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

2 + sin (x) = 5 sin (x)

2 cos (θ) + 5 = 0

sin (x) cos (x) = cos (x)

2 cos (2 θ) + 1 = 0, 0 \leq θ \leq 2 π

cot (x) sin (x) + cot (x) = 0

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