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

Problem

sin^2(y)/(1−cos(y))

Solution

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

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

(1−cos^2(y))/(1−cos(y))

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

((1−cos(y))*(1+cos(y)))/(1−cos(y))

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

1+cos(y)

Final Answer

sin^2(y)/(1−cos(y))=1+cos(y)

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