Rationalize the Denominator (sin(x)^2)/(1-cos(x))

Problem

sin^2(x)/(1−cos(x))

Solution

1. Identify the trigonometric identity for the numerator. Recall the Pythagorean identity sin^2(x)+cos^2(x)=1

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

(1−cos^2(x))/(1−cos(x))

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

((1−cos(x))*(1+cos(x)))/(1−cos(x))

4. Simplify the expression by canceling the common factor (1−cos(x)) from the numerator and the denominator.

1+cos(x)

Final Answer

sin^2(x)/(1−cos(x))=1+cos(x)

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