Simplify (sec(theta))/(csc(theta))

Problem

sec(θ)/csc(θ)

Solution

1. Use reciprocal identities to rewrite the trigonometric functions in terms of sine and cosine.

sec(θ)=1/cos(θ)

csc(θ)=1/sin(θ)

2. Substitute these identities into the original expression.

1/cos(θ)/1/sin(θ)

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

1/cos(θ)⋅sin(θ)/1

4. Combine the terms into a single fraction.

sin(θ)/cos(θ)

5. Apply the quotient identity to simplify the expression to a single trigonometric function.

tan(θ)

Final Answer

sec(θ)/csc(θ)=tan(θ)

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