If cosθ – sinθ = 2 sinθ, then cosθ

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If cosθ – sinθ = 2 sinθ, then cosθ + sinθ = ?

1. 2 cosθ
2. 2 sinθ
3. √2cosθ
4. None of these

Correct Option: C

cosθ – sinθ = 2 sinθ ..(i)
cosθ + sinθ = x ....(ii)
On squaring both the equations and adding.
2 (cos²θ + sin²θ) = 2sin²θ + x²
⇒ x² = 2 – 2 sin²θ = 2 (1 – sin²θ) = 2cos²θ
⇒ x = √2cosθ