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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
 #1
avatar+90053 
+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

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