Simplify (2csc(x)+2)(2csc(x)-2)

Problem

(2*csc(x)+2)*(2*csc(x)−2)

Solution

1. Identify the expression as a difference of squares pattern, which follows the form (a+b)*(a−b)=a2−b2

2. Apply the formula by setting a=2*csc(x) and b=2

3. Square the individual terms.

(2*csc(x))2−(2)2

4. Simplify the squares.

4*csc2(x)−4

5. Factor out the common constant 4

4*(csc2(x)−1)

6. Apply the Pythagorean identity cot2(x)+1=csc2(x) which implies csc2(x)−1=cot2(x)

4*cot2(x)

Final Answer

(2*csc(x)+2)*(2*csc(x)−2)=4*cot2(x)

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