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

Problem

cos(x)=cos(x)

Solution

1. Rearrange the equation to set it equal to zero by subtracting cos(x) from both sides.

cos(x)−cos(x)=0

2. Factor out the common term cos(x) from the expression.

cos(x)*(cos(x)−1)=0

3. Apply the zero product property to set each factor equal to zero.

cos(x)=0

cos(x)−1=0⇒cos(x)=1

4. Solve for x by finding the values where the cosine function equals 0 or 1

cos(x)=0⇒x=π/2+n*π

cos(x)=1⇒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)⇒x=π/2+n*π,2*n*π

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