Factor (sin(x)+1)^2-(sin(x)-1)^2

Problem

(sin(x)+1)2−(sin(x)−1)2

Solution

1. Identify the expression as a difference of squares in the form a2−b2 where a=sin(x)+1 and b=sin(x)−1

2. Apply the formula for the difference of squares, which is a2−b2=(a−b)*(a+b)

3. Substitute the values of a and b into the formula:

((sin(x)+1)−(sin(x)−1))*((sin(x)+1)+(sin(x)−1))

4. Simplify the terms inside the first set of parentheses by distributing the negative sign:

(sin(x)+1−sin(x)+1)

2

5. Simplify the terms inside the second set of parentheses by combining like terms:

(sin(x)+1+sin(x)−1)

2*sin(x)

6. Multiply the simplified results together:

2⋅2*sin(x)

4*sin(x)

Final Answer

(sin(x)+1)2−(sin(x)−1)2=4*sin(x)

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