Simplify (cos(a))/(sec(a))+(sin(a))/(csc(a))

Problem

cos(a)/sec(a)+sin(a)/csc(a)

Solution

1. Identify the reciprocal identities for the trigonometric functions in the denominators.

sec(a)=1/cos(a)

csc(a)=1/sin(a)

2. Substitute these identities into the original expression.

cos(a)/1/cos(a)+sin(a)/1/sin(a)

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

cos(a)⋅cos(a)+sin(a)⋅sin(a)

cos2(a)+sin2(a)

4. Apply the Pythagorean identity, which states that the sum of the squares of sine and cosine for the same angle is equal to 1.

cos2(a)+sin2(a)=1

Final Answer

cos(a)/sec(a)+sin(a)/csc(a)=1

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