Solve for x square root of 3sec(2x)=2

Problem

√(,3)*sec(2*x)=2

Solution

1. Isolate the secant function by dividing both sides of the equation by √(,3)

sec(2*x)=2/√(,3)

2. Convert the secant function to its reciprocal, the cosine function, using the identity sec(θ)=1/cos(θ)

cos(2*x)=√(,3)/2

3. Identify the general solutions for the cosine equation cos(θ)=√(,3)/2 which occur at ±π/6+2*n*π

2*x=±π/6+2*n*π

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

x=±π/12+n*π

Final Answer

√(,3)*sec(2*x)=2⇒x=±π/12+n*π

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