Simplify (1+cos(y))/(1+sec(y))

Problem

(1+cos(y))/(1+sec(y))

Solution

1. Express the secant function in terms of cosine using the reciprocal identity sec(y)=1/cos(y)

(1+cos(y))/(1+1/cos(y))

2. Find a common denominator for the expression in the denominator of the main fraction.

(1+cos(y))/(cos(y)+1)/cos(y)

3. Multiply the numerator by the reciprocal of the denominator to simplify the complex fraction.

(1+cos(y))⋅cos(y)/(cos(y)+1)

4. Cancel the common factor (1+cos(y)) from the numerator and the denominator.

cos(y)

Final Answer

(1+cos(y))/(1+sec(y))=cos(y)

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