If P={θ:sin⁡θ−cos⁡θ=2cos⁡θ} and Q={θ:sin⁡θ+cos⁡θ=2sin⁡θ} are two sets. Then,

$\begin{array}{l} \cos θ (\sqrt{2} + 1) = \sin θ \\ \Rightarrow \tan θ = \sqrt{2} + 1 and \sin θ (\sqrt{2} - 1) = \cos θ \end{array}$

$\begin{array}{l} ∴ \tan θ = \frac{1}{\sqrt{2} - 1} \times \frac{\sqrt{2} + 1}{\sqrt{2} + 1} = (\sqrt{2} + 1) \\ ∴ P = Q \end{array}$

Modal Verbs

Helping Verbs

Action Verbs

If $P = {θ : \sin θ - \cos θ = \sqrt{2} \cos θ}$ and $Q = {θ : \sin θ + \cos θ = \sqrt{2} \sin θ}$ are two sets. Then,