Solve for x 2cos(2x)+1=0

Problem

2*cos(2*x)+1=0

Solution

1. Isolate the trigonometric term by subtracting 1 from both sides and then dividing by 2.

2*cos(2*x)=−1

cos(2*x)=−1/2

2. Determine the reference angle for which the cosine is 1/2 which is π/3

3. Identify the quadrants where the cosine is negative, which are Quadrant II and Quadrant III.

2*x=π−π/3+2*k*π

2*x=π+π/3+2*k*π

4. Simplify the expressions for 2*x using a common denominator.

2*x=(2*π)/3+2*k*π

2*x=(4*π)/3+2*k*π

5. Solve for x by dividing all terms by 2, where k is any integer.

x=π/3+k*π

x=(2*π)/3+k*π

Final Answer

x=π/3+k*π,(2*π)/3+k*π

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