Solve for x cos(x)^2-cos(x)=0

Problem

cos(x)−cos(x)=0

Solution

1. Factor the common term cos(x) from the expression.

cos(x)*(cos(x)−1)=0

2. Apply the zero product property by setting each factor equal to zero.

cos(x)=0

cos(x)−1=0⇒cos(x)=1

3. Solve for x when cos(x)=0 On the unit circle, the cosine is zero at π/2 and (3*π)/2

x=π/2+n*π

4. Solve for x when cos(x)=1 On the unit circle, the cosine is one at 0

x=2*n*π

5. Combine the solutions into a general form where n is any integer.

x=π/2+n*π,2*n*π

Final Answer

cos(x)−cos(x)=0⇒x=π/2+n*π,2*n*π

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