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

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

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

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

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

Solution steps

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

Solve by substitution

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

cos (t) = 1 : t = 2 πn

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

Combine all the solutions

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

tan (x) = \frac{6}{15}

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

3 tan (θ + 4 3^{\circ}) = 2 cos (θ + 4 3^{\circ})

2 sin (θ) cos (θ) + 2 cos (θ) = 0

3 tan (2 x) = 5

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