sin theta + cos theta equal to 1 prove that sin theta minus cos theta equal to 1
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sinθ+cosθ=1
⇒(sinθ+cosθ)²=1²⇒sin²θ+cos²θ+2sinθcosθ=1
⇒1+2sinθcosθ=1 (sin²θ+cos²θ=1)
⇒2sinθcosθ=1-1=0⇒sinθcosθ=0
(sinθ-cosθ)²=sin²θ+cos²θ-2sinθcosθ=1-0=1
sinθ-cosθ=√1=1......(proved)
⇒(sinθ+cosθ)²=1²⇒sin²θ+cos²θ+2sinθcosθ=1
⇒1+2sinθcosθ=1 (sin²θ+cos²θ=1)
⇒2sinθcosθ=1-1=0⇒sinθcosθ=0
(sinθ-cosθ)²=sin²θ+cos²θ-2sinθcosθ=1-0=1
sinθ-cosθ=√1=1......(proved)
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