Solve for x cos(x)(cos(x)-1)=0

Problem

cos(x)*(cos(x)−1)=0

Solution

1. Apply the Zero Product Property by setting each factor equal to zero.

cos(x)=0

cos(x)−1=0

2. Solve the first equation cos(x)=0 for x The cosine function is zero at odd multiples of π/2

x=π/2+n*π

3. Solve the second equation by isolating the cosine term.

cos(x)=1

4. Find the values of x where cos(x)=1 This occurs at even multiples of π

x=2*n*π

5. Combine the solutions where n represents any integer (n∈ℤ.

Final Answer

cos(x)*(cos(x)−1)=0⇒x=π/2+n*π,2*n*π

Want more problems? Check here!