Solve for x sec(x)=2

Problem

sec(x)=2

Solution

1. Use the reciprocal identity to rewrite the equation in terms of the cosine function.

sec(x)=1/cos(x)

2. Substitute the identity into the original equation.

1/cos(x)=2

3. Solve for cosine by taking the reciprocal of both sides.

cos(x)=1/2

4. Identify the reference angle in the first quadrant where the cosine value is 1/2

x=π/3

5. Determine the general solutions by considering the quadrants where cosine is positive (Quadrants I and IV) and the periodicity of the cosine function.

x=π/3+2*n*π

x=(5*π)/3+2*n*π

Final Answer

sec(x)=2⇒x=π/3+2*n*π,(5*π)/3+2*n*π

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