Mathematics - Trigonometric Equation Question with Solution | TestHub

$$\begin{array}{rl}& P=\{\theta :\sin \theta -\cos \theta =\sqrt{2}\cos \theta \}\\ & \Rightarrow \cos \theta (\sqrt{2}+1)=\sin \theta \\ & \Rightarrow \tan \theta =\sqrt{2}+1\\ & Q=\{\theta :\sin \theta +\cos \theta =\sqrt{2}\sin \theta \}\\ & \Rightarrow \sin \theta (\sqrt{2}-1)=\cos \theta \\ & \Rightarrow \tan \theta =\frac{1}{\sqrt{2}-1}\times \frac{\sqrt{2}+1}{\sqrt{2}+1}\\ & =(\sqrt{2}+1)\\ & \therefore P=Q\\ & \end{array}$$