Simplify sec(2x)

Problem

sec(2*x)

Solution

1. Identify the reciprocal identity for the secant function.

sec(θ)=1/cos(θ)

2. Apply the reciprocal identity to the given expression where θ=2*x

sec(2*x)=1/cos(2*x)

3. Substitute the double-angle identity for cosine. There are three common forms for cos(2*x) cos2(x)−sin2(x) 2*cos2(x)−1 or 1−2*sin2(x) Using the primary form:

cos(2*x)=cos2(x)−sin2(x)

4. Rewrite the expression in terms of sine and cosine.

sec(2*x)=1/(cos2(x)−sin2(x))

Final Answer

sec(2*x)=1/(cos2(x)−sin2(x))

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