Let P = {θ∶ sin θ - cos θ = √2 cos θ} and Q = {θ∶ sin θ + cos θ = √2 sin θ} be two sets. Then:
P: \(\sin\theta = (\sqrt{2} + 1)\cos\theta \Rightarrow \tan\theta = \sqrt{2} + 1\)
Q: \(\cos\theta = (\sqrt{2} - 1)\sin\theta \Rightarrow \tan\theta = \frac{1}{\sqrt{2} - 1} = \sqrt{2} + 1\)
Both sets are defined by the same condition, \(\tan\theta = \sqrt{2} + 1\). So P = Q.
Answer: (D)
Reinforce your conceptual grasp with related questions from NIMCET 2018:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →