Question

If $x=\cos \theta +\sin \theta$ and $y=\cos \theta -\sin \theta$, then eliminate $\theta$ from these two relations

Answer 1

Given, $x=\cos \theta +\sin \theta$.......(1) and $y=\cos \theta -\sin \theta$......(2).

Now, (1)${}^2+$(2)${}^2$ we get,

$x^2+y^2=2({\sin }^2\theta +{\cos }^2\theta )$

or, $x^2+y^2=2$.