Solve for x cos(2x-pi/2)=1

Problem

cos(2*x−π/2)=1

Solution

1. Identify the general solution for the cosine function when it equals 1. The equation cos(θ)=1 occurs when the argument is an integer multiple of 2*π

θ=2*n*π

2. Set the argument of the cosine function equal to the general solution, where n is any integer.

2*x−π/2=2*n*π

3. Isolate the term containing x by adding π/2 to both sides of the equation.

2*x=2*n*π+π/2

4. Solve for x by dividing the entire equation by 2.

x=n*π+π/4

Final Answer

cos(2*x−π/2)=1⇒x=n*π+π/4

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