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If cosθ + sinθ = √2 cos θ, then cosθ – sinθ is    (SSC CGL 1st Sit. 2013)
  • a)
    - √2 sin θ
  • b)
    √2 sin θ
  • c)
    √2 tan θ
  • d)
    -√2 cos θ
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If cosθ + sinθ = √2 cos θ, then cosθ &nd...
cosθ + sinθ = √2 cos θ
On squaring both sides,
cos2θ + sin2θ + 2cos θ. sin θ = 2 cos2 θ
⇒ cos2θ – sin2θ = 2cosθ. cos θ
⇒ (cos θ + sin θ) (cos θ – sin θ) = 2 sin θ. cos θ
⇒ 2 cos θ (cosθ – sinθ) = 2sin θ. cos θ
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If cosθ + sinθ = √2 cos θ, then cosθ – sinθ is (SSC CGL 1st Sit. 2013)a)- √2 sin θb)√2 sin θc)√2 tan θd)-√2 cos θCorrect answer is option 'D'. Can you explain this answer?
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