Solve for x 2sec(x)+1=sec(x)+3

Problem

2*sec(x)+1=sec(x)+3

Solution

1. Isolate the sec(x) terms on one side of the equation by subtracting sec(x) from both sides.

2*sec(x)−sec(x)+1=3

sec(x)+1=3

2. Subtract 1 from both sides to solve for sec(x)

sec(x)=2

3. Rewrite the equation in terms of cos(x) using the reciprocal identity sec(x)=1/cos(x)

1/cos(x)=2

cos(x)=1/2

4. Determine the values of x that satisfy the equation within the standard interval [0,2*π)

x=π/3

x=(5*π)/3

5. Generalize the solution by adding multiples of the period 2*π*n where n is an integer.

x=π/3+2*π*n

x=(5*π)/3+2*π*n

Final Answer

x=π/3+2*π*n,(5*π)/3+2*π*n

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