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

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

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

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

x = π + 2 πn, x = 2 πn

Solution steps

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

Solve by substitution

cos (x) = - 1, cos (x) = 1

cos (x) = - 1 : x = π + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = π + 2 πn, x = 2 πn

tan (2 θ) = 1, 0^{\circ} \leq θ \leq 36 0^{\circ}

2 cos (θ) + 2 = 0, 0 \leq θ \leq 2 π

3 tan (\frac{θ}{2}) - 1 = 0

tan (\frac{x}{2}) = 3, 0 \leq x < 2 π

sin (x) = \frac{4}{cos ( x )}

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