What is the general solution for 3cos^2(x)-2cos(x)-1=0 ?

The general solution for 3cos^2(x)-2cos(x)-1=0 is x=2pin,x=1.91063…+2pin,x=-1.91063…+2pin

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3cos^2(x)-2cos(x)-1=0

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

x = 2 πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = 1, cos (x) = - \frac{1}{3}

cos (x) = 1 : x = 2 πn

cos (x) = - \frac{1}{3} : x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

Combine all the solutions

x = 2 πn, x = arccos (- \frac{1}{3}) + 2 πn, x = - arccos (- \frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 2 πn, x = 1.91063 \dots + 2 πn, x = - 1.91063 \dots + 2 πn

x, y - \frac{1}{cos ( x )} = 0

2 sin (x) - cos (2 x) = 0

sin^{2} (x) sec (x) = tan^{2} (x)

cos (2 x + \frac{π}{3}) = - \frac{1}{2}

sec (θ + 2 0^{\circ}) = 3

What is the general solution for 3cos^2(x)-2cos(x)-1=0 ?
The general solution for 3cos^2(x)-2cos(x)-1=0 is x=2pin,x=1.91063…+2pin,x=-1.91063…+2pin