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Question
cos θ/(1 - tan θ) + sin θ/(1 - cot θ) = sin θ + cos θ
cos θ/(1 - tan θ) + sin θ/(1 - cot θ) = sin θ + cos θ
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Solution
G = (cos θ/(1 - tan θ)) + (sin θ/(1 - cot θ))
G = (cos θ/(1 - sin θ/cos θ)) + (sin θ/(1 - cos θ/sin θ))
G = (cos² θ/(cos θ - sin θ)) + (sin² θ/(sin θ - cos θ))
G = (cos² θ/(cos θ - sin θ)) - (sin² θ/(cos θ - sin θ))
G = (cos θ - sin θ)(cos θ + sin θ) /(cos θ - sin θ)
G = cos θ + sin θ
G = (cos θ/(1 - sin θ/cos θ)) + (sin θ/(1 - cos θ/sin θ))
G = (cos² θ/(cos θ - sin θ)) + (sin² θ/(sin θ - cos θ))
G = (cos² θ/(cos θ - sin θ)) - (sin² θ/(cos θ - sin θ))
G = (cos θ - sin θ)(cos θ + sin θ) /(cos θ - sin θ)
G = cos θ + sin θ
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