Prove that cos/(1-tan) + sin/(1-cot) = sin + cos

1.	Prove that cos/(1-tan) + sin/(1-cot) = sin + cos
Answer» Next GurukulLearner\'s SectionWikiK-12 WikiAssessmentAssessmentsForumQ&A ForumEducator\'s SectionMOOCMOOCsJoin Experts PanelJoin Experts PanelNext WorldThe Next WorldAcademic Questions & Answers ForumVijaySep 7, 2014Prove that cos A / (1 - tan A) + sin A /(1 - cot A) = sin A + cos AProve that cos A / (1 - tan A) + sin A /(1 - cot A) = sin A + cos A question_answer Answers(1)personChandrakant Mane Member since Apr 1, 2014Sol: 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.

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