if cos theta+sin theta=√2,then costheta -sin theta=
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Answer:
cosθ-sinθ = 0
Step-by-step explanation:
Given, cosθ+sinθ = √2
consider, (cosθ+sinθ)² + (cosθ-sinθ)²
= cos²θ+2sinθcosθ+sin²θ + cos²θ-2sinθcosθ+sin²θ
= cos²θ + cos²θ+sin²θ+sin²θ
= 2 (cos²θ+sin²θ)
= 2
=> (cosθ+sinθ)² + (cosθ-sinθ)² = 2
ie, √2² + (cosθ-sinθ)² = 2 (given cosθ+sinθ=√2)
=> 2 + (cosθ-sinθ)² = 2
=> (cosθ-sinθ)² = 2 - 2 = 0
=> cosθ-sinθ = 0
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