What is the general solution for cos(x)+|cos(x)|=1 ?

The general solution for cos(x)+|cos(x)|=1 is x= pi/3+2pin,x=(5pi)/3+2pin

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cos(x)+|cos(x)|=1

cos (x) + ∣ cos (x) ∣ = 1

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

cos (x) + ∣ cos (x) ∣ = 1

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 sin (\frac{π}{3} - x) = 1

9 tan^{2} (z) cos (z) = 3 cos (z)

sin (2 x) sin (4 x) = cos (2 x) cos (4 x)

\frac{1}{sec ( θ )} = - \frac{7}{25}

3 tan^{3} (x) - 2 tan^{2} (x) - 32 tan (x) - 32 = 0

What is the general solution for cos(x)+|cos(x)|=1 ?
The general solution for cos(x)+|cos(x)|=1 is x= pi/3+2pin,x=(5pi)/3+2pin