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

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

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

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

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

Solution steps

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

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

arcsin (- \frac{1}{2})

csc (- \frac{5 π}{6})

tan (\frac{5 π}{6})

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

cos (\frac{5 π}{8})

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