Simplify

Problem

√(,(1−sin(θ))*(1+sin(θ)))

Solution

1. Identify the difference of squares pattern (a−b)*(a+b)=a2−b2 inside the square root.

2. Expand the product using this identity where a=1 and b=sin(θ)

√(,1−sin2(θ))

3. Simplify the expression using the Pythagorean identity sin2(θ)+cos2(θ)=1 which implies 1−sin2(θ)=cos2(θ)

√(,cos2(θ))

4. Apply the property of square roots √(,x2)=|x| to find the final simplified form.

|cos(θ)|

Final Answer

√(,(1−sin(θ))*(1+sin(θ)))=|cos(θ)|

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