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CBSE Class 10 Answered

prove the following: 1 / cosec theta-cot theta - 1/ sin theta = 1 / sin theta - 1/ cosec theta + cot theta
Asked by nisha_vini29 | 07 Sep, 2015, 10:02: PM
answered-by-expert Expert Answer

C o n s i d e r space t h e space L H S space o f space t h e space g i v e n space e q u a t i o n colon L H S equals fraction numerator 1 over denominator cos e c theta minus c o t theta end fraction minus fraction numerator 1 over denominator sin theta end fraction space space space space space space space equals fraction numerator 1 over denominator c o s e c theta minus c o t theta end fraction cross times fraction numerator c o s e c theta plus c o t theta over denominator c o s e c theta plus c o t theta end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator c o s e c theta plus c o t theta over denominator c o s e c squared theta minus c o t squared theta end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator c o s e c theta plus c o t theta over denominator 1 end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator s i n theta open parentheses cos e c theta plus c o t theta close parentheses minus 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator 1 plus cos theta minus 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction plus fraction numerator c o s theta over denominator s i n theta end fraction minus fraction numerator 1 over denominator s i n theta end fraction space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction plus c o t theta minus cos e c theta space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction minus open parentheses cos e c theta minus c o t theta close parentheses space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction minus open parentheses c o s e c theta minus c o t theta close parentheses cross times fraction numerator open parentheses c o s e c theta plus c o t theta close parentheses over denominator open parentheses c o s e c theta plus c o t theta close parentheses end fraction space space space space space space space equals fraction numerator 1 over denominator s i n theta end fraction minus fraction numerator 1 over denominator open parentheses c o s e c theta plus c o t theta close parentheses end fraction H e n c e space p r o v e d.

Answered by | 09 Sep, 2015, 06:08: PM

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