Question

Please solve this question. The best answer will be awarded as brainliest

Answer 1

CosΘ-SinΘ=$\sqrt{2}$sinΘ

CosΘ=$\sqrt{2}$Θ+SinΘ

CosΘ=($\sqrt{2}+1$)sinΘ

($\sqrt{2}-1$)cosΘ=($\sqrt{2}-1$)($\sqrt{2}+1$)sinΘ

$\sqrt{2}-1$)cosΘ=(2-1)sinΘ

$\sqrt{2}-1$)cosΘ=sinΘ

$\sqrt{2} cos$Θ-cosΘ=sinΘ

$\sqrt{2} cos$Θ=sinΘ+cosΘ

       

Answer 2

Given Equation is cosθ - sinθ = √2 sin θ.

On Squaring both sides, we get

⇒ (cosθ - sinθ)² = (√2 sinθ)²

⇒ cos²θ + sin²θ - 2 cosθsinθ = 2 sin²θ

⇒ cos²θ + sin²θ - 2 cosθsinθ = sin²θ + sin²θ

⇒ cos²θ - 2 cosθsinθ = sin²θ

⇒ 2 cos²θ - cos²θ - 2 cosθsinθ = sin²θ

⇒ 2 cos²θ = cos²θ + sin²θ + 2 cosθsinθ

⇒ 2 cos²θ = (cosθ + sinθ)²

⇒ √2 cosθ = cos θ + sin θ.

Hope this helps!