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

The general solution for 2cos^2(w)-cos(w)-1=0 is w=2pin,w=(2pi)/3+2pin,w=(4pi)/3+2pin

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2cos^2(w)-cos(w)-1=0

2 cos^{2} (w) - cos (w) - 1 = 0

w = 2 πn, w = \frac{2 π}{3} + 2 πn, w = \frac{4 π}{3} + 2 πn

Solution steps

2 cos^{2} (w) - cos (w) - 1 = 0

Solve by substitution

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

cos (w) = 1 : w = 2 πn

cos (w) = - \frac{1}{2} : w = \frac{2 π}{3} + 2 πn, w = \frac{4 π}{3} + 2 πn

Combine all the solutions

w = 2 πn, w = \frac{2 π}{3} + 2 πn, w = \frac{4 π}{3} + 2 πn

3 csc (θ) - 3 = 0

2 sin (x) + (sin (x))^{2} = 0

2 cos (x) + 1 = 3, 0 \leq x \leq 2 π

1 - 2 sin (2 x) = 0

2 sin (x) + \frac{1}{sin ( x )} = 0

What is the general solution for 2cos^2(w)-cos(w)-1=0 ?
The general solution for 2cos^2(w)-cos(w)-1=0 is w=2pin,w=(2pi)/3+2pin,w=(4pi)/3+2pin