Question

If cos 0 + sin 0 = √2 cos q, then show that cos 0 - sin 0 =√2​

Answer 1

Answer:

Step-by-step explanation:

Cosθ  + Sinθ  = √2 Cosθ

Squaring both sides

=> Cos²θ  + Sin²θ + 2CosθSinθ = 2Cos²θ

=> 2CosθSinθ = Cos²θ - Sin²θ

Cos²  + Sin²θ   = 1

Subtracting 2CosθSinθ from both sides

=> Cos²  + Sin²θ - 2CosθSinθ = 1 -  2CosθSinθ

=> (Cosθ  - Sinθ)² = 1 -  2CosθSinθ

using  2CosθSinθ = Cos²θ - Sin²θ

=>  (Cosθ  - Sinθ)²  = 1 - (Cos²θ - Sin²θ)

=>   (Cosθ  - Sinθ)²  = 1 - Cos²θ + Sin²θ

=>   (Cosθ  - Sinθ)²  = Sin²θ + Sin²θ

=> (Cosθ  - Sinθ)²  = 2Sin²θ

=> Cosθ  - Sinθ  = √2 Sinθ

QED

Proved

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