Question

If $\sin \theta +\cos \theta =1$, then the value of $\sin \theta \cos \theta$ is

Answer 1

$\sin \theta +\cos \theta =1$ or squaring both sides
${\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =1$
i.e. $1+2\sin \theta \cos \theta =1$
or $2\sin \theta \cos \theta =0$ or $\sin \theta \cos \theta =0$