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If Sin^2x + Cos^2x = 1 

then why doesnt Sinx + Cosx = 1

when you could square root both sides??

 Sep 26, 2014

Best Answer 

 #2
avatar+118716 
+13

Sin^2x + Cos^2x = 1

that is a good question why don't we square sinx+cosx and see what happens.  

 

(Sinx+Cosx)2=sin2x+cos2x+2sinxcosx=1+2sinxcosx

 

So

 

(sinx+cosx)2=1+2sinxcosx$Takingthesquarerootofbothsidesweget$sinx+cosx=±1+2sinxcosx

 

It can only equal one if   2sinxcosx=0       and that doesn't happen very often.        

 Sep 26, 2014
 #1
avatar+23254 
+13

√(x²+y²) ≠ x + y       (Except for rare cases.)

For instance: √(3²+4²) = √(9+16) = √25 = 5

But: if √(x²+y²) = x + y, then √(3²+4²) would equal 3 + 4 = 7 (which it doesn't).

 Sep 26, 2014
 #2
avatar+118716 
+13
Best Answer

Sin^2x + Cos^2x = 1

that is a good question why don't we square sinx+cosx and see what happens.  

 

(Sinx+Cosx)2=sin2x+cos2x+2sinxcosx=1+2sinxcosx

 

So

 

(sinx+cosx)2=1+2sinxcosx$Takingthesquarerootofbothsidesweget$sinx+cosx=±1+2sinxcosx

 

It can only equal one if   2sinxcosx=0       and that doesn't happen very often.        

Melody Sep 26, 2014

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