+0  
 
0
148
1
avatar

Perform the mlutiplication and use the fundamental identiteis to simplify. 

 

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

 

answer: 4cot^2x

But HOW???

Guest Apr 23, 2017

Best Answer 

 #1
avatar+4808 
+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

hectictar  Apr 23, 2017
Sort: 

1+0 Answers

 #1
avatar+4808 
+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

10 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details