Question

...............maths trigonometry

Answer 1

Step-by-step explanation:

cosθ + sinθ = √2cosθ

Square on both sides.

(cosθ + sinθ)² = (√2cosθ)²

cos²θ + sin²θ + 2cosθsinθ = 2cos²θ

sin²θ = 2cos²θ - 2cosθsinθ

sin²θ = cos²θ - 2sinθcosθ

'Add sin²θ on both sides'

sin²θ + sin²θ = cos²θ + sin²θ - 2sinθcosθ

2sin²θ = (cosθ - sinθ)²

cosθ - sinθ = √2sinθ

Hope it helps you.

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