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

The general solution for |cos(x)|=-1 is No Solution for x\in\mathbb{R}

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|cos(x)|=-1

∣ cos (x) ∣ = - 1

No Solution for x \in R

Solution steps

∣ cos (x) ∣ = - 1

Solve by substitution

∣ cos (x) ∣ = - 1

Let:

cos (x) = u

∣ u ∣ = - 1

∣ u ∣ = - 1 :

No Solution for

u \in R

∣ u ∣ = - 1

Absolute value cannot be less than 0

No Solution for u \in R

Substitute back

u = cos (x)

No Solution for cos (x) \in R

No Solution for cos (x) \in R

cos (x) =

No Solution

: x = arccos (No Solution) + 2 πn, x = - arccos (No Solution) + 2 πn

cos (x) = No Solution

Apply trig inverse properties

cos (x) = No Solution

General solutions for

cos (x) =

No Solution

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

x = arccos (No Solution) + 2 πn, x = - arccos (No Solution) + 2 πn

x = arccos (No Solution) + 2 πn, x = - arccos (No Solution) + 2 πn

Combine all the solutions

x = arccos (No Solution) + 2 πn, x = - arccos (No Solution) + 2 πn

Since the equation is undefined for:

arccos (No Solution) + 2 πn, - arccos (No Solution) + 2 πn

No Solution for x \in R

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What is the general solution for |cos(x)|=-1 ?
The general solution for |cos(x)|=-1 is No Solution for x\in\mathbb{R}