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

Problem

sec(x)/tan(x)

Solution

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

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

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

1/cos(x)⋅cos(x)/sin(x)

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

1/sin(x)

4. Apply the reciprocal identity csc(x)=1/sin(x) to reach the simplest form.

csc(x)

Final Answer

sec(x)/tan(x)=csc(x)

Want more problems? Check here!