Simplify (cos(y)^2)/(1-sin(y))

Problem

cos^2(y)/(1−sin(y))

Solution

1. Identify the Pythagorean identity for the numerator, which states that cos^2(y)+sin^2(y)=1

2. Substitute the identity cos^2(y)=1−sin^2(y) into the expression.

(1−sin^2(y))/(1−sin(y))

3. Factor the numerator using the difference of squares formula, a^2−b^2=(a−b)*(a+b)

((1−sin(y))*(1+sin(y)))/(1−sin(y))

4. Simplify the fraction by canceling the common factor (1−sin(y)) from the numerator and the denominator.

1+sin(y)

Final Answer

cos^2(y)/(1−sin(y))=1+sin(y)

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