Solve for x cos(2x)=-1

Problem

cos(2*x)=−1

Solution

1. Identify the general solution for the cosine function when it equals −1 The cosine of an angle is −1 when the angle is an odd multiple of π

cos(θ)=−1⇒θ=π+2*k*π

2. Substitute the argument of the cosine function, which is 2*x into the general solution formula, where k is any integer.

2*x=π+2*k*π

3. Isolate x by dividing both sides of the equation by 2

x=(π+2*k*π)/2

4. Simplify the expression to find the final form of the solution.

x=π/2+k*π

Final Answer

cos(2*x)=−1⇒x=π/2+k*π,k∈ℤ

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