Simplify (sec(theta))/(tan(theta))

Problem

sec(θ)/tan(θ)

Solution

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

sec(θ)/tan(θ)=1/cos(θ)/sin(θ)/cos(θ)

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

1/cos(θ)⋅cos(θ)/sin(θ)

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

1/sin(θ)

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

csc(θ)

Final Answer

sec(θ)/tan(θ)=csc(θ)

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