If Cos θ + Sin θ = √2 Cos θ, find the value of (cos θ - Sinθ)
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Correct answer: A
Explanation
The correct answer is option 1 i.e. √2 sin θ.
Given that
If Cos θ + Sin θ = √2 Cos θ
Square on both sides
⇒ (Cos θ + Sin θ)2 = (√2 Cos θ)2
⇒ Cos2 θ + Sin2 θ + 2 Cos θ Sin θ = 2 Cos2 θ
⇒ (Cos θ - Sinθ)2 = 2 - 2Cos2 θ = 2 Sin2 θ
⇒ Cos θ - Sinθ = √2 sin θ