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

Problem

(1−cos2(x))/sin(x)

Solution

1. Identify the Pythagorean identity sin2(x)+cos2(x)=1

2. Rearrange the identity to solve for the numerator, which gives 1−cos2(x)=sin2(x)

3. Substitute the identity into the original expression.

sin2(x)/sin(x)

4. Simplify the fraction by canceling one factor of sin(x) from the numerator and denominator.

sin(x)

Final Answer

(1−cos2(x))/sin(x)=sin(x)

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