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

Feb 3, 2017

Many counterexamples can be given to show that $\sin x + \cos x = 1$ is not an identity.
One such is obtained by choosing $x = \frac{\pi}{4}$
The L.H.S.
$= \sin \left(\frac{\pi}{4}\right) + \cos \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} \ne 1$
=The R.H.S.