Simplify sec(-x)

Problem

sec(−x)

Solution

1. Identify the parity of the trigonometric function. The secant function is the reciprocal of the cosine function.

2. Apply the identity for the cosine of a negative angle, which is cos(−x)=cos(x) because cosine is an even function.

3. Substitute this property into the definition of secant:

sec(−x)=1/cos(−x)

4. Simplify the expression using the even property of cosine:

1/cos(−x)=1/cos(x)

5. Recognize that the resulting expression is the definition of sec(x)

Final Answer

sec(−x)=sec(x)

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