Simplify (sec(x))/(cos(x))

Problem

sec(x)/cos(x)

Solution

1. Identify the trigonometric identity for the secant function.

sec(x)=1/cos(x)

2. Substitute the identity into the numerator of the original expression.

1/cos(x)/cos(x)

3. Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.

1/cos(x)⋅1/cos(x)

4. Multiply the terms to reach the final simplified form.

1/cos2(x)

5. Apply the reciprocal identity to express the result in terms of the secant function.

sec2(x)

Final Answer

sec(x)/cos(x)=sec2(x)

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