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

Problem

1/sin(θ)−1/cos(θ)

Solution

1. Identify the common denominator for the two fractions, which is sin(θ)*cos(θ)

2. Rewrite each fraction with the common denominator by multiplying the first term by cos(θ)/cos(θ) and the second term by sin(θ)/sin(θ)

3. Combine the numerators over the single common denominator.

4. Apply reciprocal identities if desired, noting that 1/sin(θ)=csc(θ) and 1/cos(θ)=sec(θ)

Final Answer

1/sin(θ)−1/cos(θ)=(cos(θ)−sin(θ))/(sin(θ)*cos(θ))

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