Simplify square root of 1-cos(x)^2

Problem

√(,1−cos^2(x))

Solution

1. Identify the trigonometric identity for the expression inside the square root.

2. Apply the identity sin^2(x)+cos^2(x)=1 which can be rearranged to 1−cos^2(x)=sin^2(x)

3. Substitute the identity into the original expression.

√(,sin^2(x))

4. Simplify the square root of a squared term, noting that √(,a^2)=|a|

|sin(x)|

Final Answer

√(,1−cos^2(x))=|sin(x)|

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