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

Problem

√(,1−sin2(x))

Solution

1. Identify the fundamental trigonometric identity relating sine and cosine.

sin2(x)+cos2(x)=1

2. Rearrange the identity to solve for the expression under the radical.

cos2(x)=1−sin2(x)

3. Substitute the identity into the original square root expression.

√(,cos2(x))

4. Simplify the square root of a squared term using the absolute value property.

|cos(x)|

Final Answer

√(,1−sin2(x))=|cos(x)|

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