Simplify

Problem

cos(θ)/sec(θ)+sin(θ)/csc(θ)

Solution

1. Identify the reciprocal identities for the denominator terms.

sec(θ)=1/cos(θ)

csc(θ)=1/sin(θ)

2. Substitute these identities into the original expression.

cos(θ)/1/cos(θ)+sin(θ)/1/sin(θ)

3. Simplify the complex fractions by multiplying the numerators by the reciprocals of the denominators.

cos(θ)⋅cos(θ)+sin(θ)⋅sin(θ)

cos2(θ)+sin2(θ)

4. Apply the Pythagorean identity.

cos2(θ)+sin2(θ)=1

Final Answer

cos(θ)/sec(θ)+sin(θ)/csc(θ)=1

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