+0  
 
+1
299
2
avatar

I'm sorry, but two more questions please:)

 

sin(x) - sin(x) * cos^2(x)

 

 

 

sin^4(x) - cos^4(x) divided by sin^2(x) - cos^2(x)

Guest Mar 29, 2017
 #1
avatar+87294 
+2

sin(x) - sin(x) * cos^2(x)  =

 

sin x  - sin x  *  ( 1 - sin^2 x)  =

 

sinx  -  sin x  + sin^3 x  =

 

sin^3 x

 

 

 

sin^4(x) - cos^4(x) divided by sin^2(x) - cos^2(x)

 

Factor   sin^4 x - cos^4x   as      

 

[sin^2 x + cos ^2 x] [ sin^2 x - cos^2 x ]  /  [sin^2 x - cos^2 x ]   =

 

sin^2 x  + cos^2 x   =

 

1

 

 

 

cool cool cool

CPhill  Mar 29, 2017
 #2
avatar+92775 
+2

sin(x) - sin(x) * cos^2(x)

\(sin(x) - sin(x) * cos^2(x)\\ =sin(x) (1- cos^2(x))\\ =sin(x) sin^2(x)\\ =sin^3(x)\\ \)

 

 

sin^4(x) - cos^4(x) divided by sin^2(x) - cos^2(x)

 

\(\frac{sin^4(x) - cos^4(x) }{sin^2(x) - cos^2(x)}\\ =\frac{(sin^2(x) - cos^2(x))(sin^2(x) + cos^2(x)) }{sin^2(x) - cos^2(x)}\\ =\frac{sin^2(x) - cos^2(x)}{sin^2(x) - cos^2(x)}\\~\\ =1 \qquad where \;\;\; x\ne \frac{\pi+2n\pi}{4} \;\;\;n\in Z\)

Melody  Mar 29, 2017

16 Online Users

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.