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Perform the mlutiplication and use the fundamental identiteis to simplify. 

 

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

 

answer: 4cot^2x

But HOW???

 Apr 23, 2017

Best Answer 

 #1
avatar+9460 
+3

Multiply each thing in the first set of parenthesees by each thing in the second set of parenthesees and add the products together.

 

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

 = (2csc x)(2csc x) + (2csc x)(-2) + (2)(2csc x) + (2)(-2)

= 4csc2x - 4csc x + 4 csc x - 4

= 4csc2x - 4

 

Factor out a 4.

= 4(csc2x - 1)

 

Rewrite like this.

\(=4(\frac{1}{\sin^2x}-1)=4(\frac{1}{\sin^2x}-\frac{\sin^2x}{\sin^2x})=4(\frac{1-\sin^2x}{\sin^2x})\)

 

Then, use the Pythagorean identity that says sin2 + cos2 = 1

\(=4(\frac{cos^2x}{sin^2x})\)

 

= 4cot2x

 Apr 23, 2017
 #1
avatar+9460 
+3
Best Answer

Multiply each thing in the first set of parenthesees by each thing in the second set of parenthesees and add the products together.

 

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

 = (2csc x)(2csc x) + (2csc x)(-2) + (2)(2csc x) + (2)(-2)

= 4csc2x - 4csc x + 4 csc x - 4

= 4csc2x - 4

 

Factor out a 4.

= 4(csc2x - 1)

 

Rewrite like this.

\(=4(\frac{1}{\sin^2x}-1)=4(\frac{1}{\sin^2x}-\frac{\sin^2x}{\sin^2x})=4(\frac{1-\sin^2x}{\sin^2x})\)

 

Then, use the Pythagorean identity that says sin2 + cos2 = 1

\(=4(\frac{cos^2x}{sin^2x})\)

 

= 4cot2x

hectictar Apr 23, 2017

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