If cos θ + sin θ = √2 cos θ, find cos θ - sin θ
Answers
Answered by
2
Answer:
Wehave,
→cosθ +sin θ =√2cos θ .
[ Squaring both side, we get ] .
⇒(cosθ+sinθ)²=2cos²θ.
⇒cos²θ+sin²θ+2cosθsinθ=2cos².
⇒sin²θ+2cosθsinθ=2cos²θ-cos²θ.
⇒sin²θ+2cosθsinθ=cos²θ.
⇒cos²θ-2cosθsinθ=sin²θ.
[ Adding sin²θ both side, we get ] .
⇒cos²θ-2cosθsinθ+sin²θ=sin²θ+sin²θ.
⇒(cosθ-sinθ)²=2sin²θ.
⇒cosθ-sinθ=√(2sin²θ).
∴cosθ-sinθ=√2sinθ.
Hence,itis proved.
Similar questions