Simplify 1-sec(x)

Problem

1−sec(x)

Solution

1. Identify the trigonometric identity for the secant function.

2. Substitute the reciprocal identity sec(x)=1/cos(x) into the expression.

1−1/cos(x)

3. Find a common denominator to combine the terms.

cos(x)/cos(x)−1/cos(x)

4. Combine the numerators over the common denominator.

(cos(x)−1)/cos(x)

Final Answer

1−sec(x)=(cos(x)−1)/cos(x)

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