Simplify (1/(cos(theta)))/(1/(sin(theta)))

Problem

1/cos(θ)/1/sin(θ)

Solution

1. Identify the expression as a complex fraction where one fraction is divided by another.

2. Apply the rule for dividing fractions, which states that dividing by a fraction is equivalent to multiplying by its reciprocal.

1/cos(θ)/1/sin(θ)=1/cos(θ)⋅sin(θ)/1

3. Multiply the numerators and denominators to combine the terms into a single fraction.

(1⋅sin(θ))/(cos(θ)⋅1)=sin(θ)/cos(θ)

4. Substitute the trigonometric identity for the ratio of sine to cosine.

sin(θ)/cos(θ)=tan(θ)

Final Answer

1/cos(θ)/1/sin(θ)=tan(θ)

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