Question

How do you prove that `sinx+cosx=1` is not an identity by showing a counterexample?

Answer 1

Many counterexamples can be given to show that `sinx+cosx=1` is not an identity.
One such is obtained by choosing `x=pi/4`
The L.H.S.
`=sin(pi/4)+cos(pi/4)=1/sqrt2+1/sqrt2=2/sqrt2=sqrt2ne1`
=The R.H.S.