Simplify sec(arccos(u))

Problem

sec(arccos(u))

Solution

1. Identify the relationship between the trigonometric functions. The expression involves the secant of an inverse cosine.

2. Recall the definition of the secant function. The secant of an angle is the reciprocal of the cosine of that same angle.

sec(θ)=1/cos(θ)

3. Substitute the inner expression arccos(u) for θ

sec(arccos(u))=1/cos(arccos(u))

4. Apply the property of inverse functions. For any value u in the domain of the inverse cosine, cos(arccos(u))=u

1/cos(arccos(u))=1/u

Final Answer

sec(arccos(u))=1/u

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