Let P = $P=\{\theta :sin \theta –cos \theta =\sqrt{2}cos \theta \} and \{Q=\theta :sin \theta +cos \theta =\sqrt{2}sin \theta \}$ be two sets, then

$\sin \theta – \cos \theta =\sqrt{ 2} \cos \theta$

$\iff \sin \theta = ( \sqrt{2 +1} ) \cos \theta$

$\iff \cos \theta = ( \sqrt{2 -1 }) \sin \theta$

$\iff \sin \theta + \cos \theta = \sqrt{2} \sin \theta$

$\Rightarrow P =Q$