If Sin^2x + Cos^2x = 1
then why doesnt Sinx + Cosx = 1
when you could square root both sides??
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.
√(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).
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.