Question

prove that Cos A minus Sin A + 1 / Cos A + Sin A minus 1 is equal to Cos A + cot a

Answer 1

Prove that Cos A minus Sin A + 1 / Cos A + Sin A minus 1 is equal to Cos A + cot a
cos A / (1 - tan A) + sin A /(1 - cot A) = sin A + cos A       

LHS = cos A / (1 - tan A) + sin A /(1 - cot A)
       = cos2 A / (cos A - sin A) + sin2 A / (sin A - cos A)
       = cos2 A / (cos A - sin A) - sin2 A / (cos A - sin A)
       = (cos2 A - sin2 A) / (cos A - sin A)
       = (cos A + sin A) (cos A - sin A) / (cos A - sin A)
       = (cos A + sin A).

Hence proved.

Answer 2

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