+0  
 
0
295
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+7324 
+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
 #1
avatar+7324 
+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

38 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.