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

Problem

sin2(θ)/(1−cos(θ))

Solution

1. Identify the Pythagorean identity for the numerator, which states that sin2(θ)+cos2(θ)=1

2. Substitute the identity sin2(θ)=1−cos2(θ) into the expression.

(1−cos2(θ))/(1−cos(θ))

3. Factor the numerator using the difference of squares formula, a2−b2=(a−b)*(a+b)

((1−cos(θ))*(1+cos(θ)))/(1−cos(θ))

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

1+cos(θ)

Final Answer

sin2(θ)/(1−cos(θ))=1+cos(θ)

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