Simplify (tan(x))/(sec(-x))

Problem

tan(x)/sec(−x)

Solution

1. Apply the even-odd identity for the secant function, which states that sec(−x)=sec(x)

2. Rewrite the expression using the identity from the previous step.

tan(x)/sec(x)

3. Express in terms of sine and cosine by substituting tan(x)=sin(x)/cos(x) and sec(x)=1/cos(x)

sin(x)/cos(x)/1/cos(x)

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

sin(x)/cos(x)⋅cos(x)/1

5. Cancel the common factor of cos(x) from the numerator and the denominator.

sin(x)

Final Answer

tan(x)/sec(−x)=sin(x)

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