Solve for x cos(x)^2-1=0

Problem

cos(x)−1=0

Solution

1. Isolate the squared trigonometric term by adding 1 to both sides of the equation.

cos(x)=1

2. Take the square root of both sides to solve for cos(x) remembering to include both the positive and negative roots.

cos(x)=±√(,1)

cos(x)=±1

3. Identify the angles on the unit circle where the cosine value is either 1 or −1

cos(x)=1⇒x=0,2*π,4*π,…

cos(x)=−1⇒x=π,3*π,5*π,…

4. Generalize the solution by combining these points into a single expression using an integer n

x=n*π

Final Answer

cos(x)−1=0⇒x=n*π

Want more problems? Check here!