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

Problem

tan(x)/sec(x)

Solution

1. Rewrite the trigonometric functions in terms of sine and cosine using the fundamental identities tan(x)=sin(x)/cos(x) and sec(x)=1/cos(x)

tan(x)/sec(x)=sin(x)/cos(x)/1/cos(x)

2. Multiply the numerator by the reciprocal of the denominator to simplify the complex fraction.

sin(x)/cos(x)⋅cos(x)/1

3. 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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