Simplify

Problem

√(,(1−sin(θ))*(1+sin(θ)))

Solution

1. Identify the difference of squares pattern (a−b)*(a+b)=a^2−b^2 inside the square root.

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

√(,1^2−sin^2(θ))

3. Simplify the expression using the Pythagorean identity sin^2(θ)+cos^2(θ)=1 which implies 1−sin^2(θ)=cos^2(θ)

√(,cos^2(θ))

4. Apply the property of square roots √(,x^2)=|x| to find the final simplified form.

|cos(θ)|

Final Answer

√(,(1−sin(θ))*(1+sin(θ)))=|cos(θ)|

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