+0  
 
0
28
1
avatar+369 

What two common identities are most useful for proving that  2cos^2x = cos2x+1 

 

I went off starting that cos2x is an identity but stuff wasn't working out...

 
Julius  Dec 5, 2017
Sort: 

1+0 Answers

 #1
avatar+79819 
+3

 

One thing about these identities is that there may be more than one way of proving them

 

So...let's try this....

 

 2cos^2 (x) = cos(2x) +1 

 

2( 1 - sin^2 (x))  =  cos (x + x)  + 1

 

2 - 2sin^2 (x)    =   cos(x)cos(x) - sin(x)sin(x)  + 1      subtract 1 from both sides

 

1 - 2sin^2(x) = cos^2(x) - sin^2(x)          add 2 sin^2x to both sides

 

1  =  cos^2(x)  + sin^2(x)        which is true

 

 

cool cool cool

 
CPhill  Dec 5, 2017

9 Online Users

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