Tan theta/sec theta+1 + cot theta/cosec theta+1 = cosec theta+sec theta -sec theta×tan theta

Asked by vans75a | 28th Sep, 2015, 09:17: PM

Expert Answer:

C o n s i d e r space t h e space e x p r e s s i o n space fraction numerator tan theta over denominator s e c theta plus 1 end fraction plus fraction numerator c o t theta over denominator cos e c theta plus 1 end fraction colon fraction numerator t a n theta over denominator s e c theta plus 1 end fraction plus fraction numerator c o t theta over denominator c o s e c theta plus 1 end fraction equals fraction numerator t a n theta over denominator s e c theta plus 1 end fraction cross times fraction numerator s e c theta minus 1 over denominator s e c theta minus 1 end fraction plus fraction numerator c o t theta over denominator c o s e c theta plus 1 end fraction cross times fraction numerator c o s e c theta minus 1 over denominator c o s e c theta minus 1 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator t a n theta open parentheses s e c theta minus 1 close parentheses over denominator s e c squared theta minus 1 end fraction plus fraction numerator c o t theta open parentheses c o s e c theta minus 1 close parentheses over denominator c o s e c squared theta minus 1 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator t a n theta open parentheses s e c theta minus 1 close parentheses over denominator tan squared theta end fraction plus fraction numerator c o t theta open parentheses c o s e c theta minus 1 close parentheses over denominator c o t squared theta end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses s e c theta minus 1 close parentheses over denominator t a n theta end fraction plus fraction numerator open parentheses c o s e c theta minus 1 close parentheses over denominator c o t theta end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses begin display style fraction numerator 1 over denominator cos theta end fraction end style minus 1 close parentheses over denominator begin display style fraction numerator sin theta over denominator cos theta end fraction end style end fraction plus fraction numerator open parentheses begin display style fraction numerator 1 over denominator sin theta end fraction minus 1 end style close parentheses over denominator begin display style fraction numerator cos theta over denominator sin theta end fraction end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses begin display style fraction numerator 1 minus cos theta over denominator c o s theta end fraction end style close parentheses over denominator begin display style fraction numerator s i n theta over denominator c o s theta end fraction end style end fraction plus fraction numerator open parentheses begin display style fraction numerator 1 minus sin theta over denominator s i n theta end fraction end style close parentheses over denominator begin display style fraction numerator c o s theta over denominator s i n theta end fraction end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 minus c o s theta over denominator begin display style s i n theta end style end fraction plus fraction numerator 1 minus s i n theta over denominator begin display style c o s theta end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator cos theta open parentheses 1 minus cos theta close parentheses plus s i n theta open parentheses 1 minus s i n theta close parentheses over denominator begin display style s i n theta c o s theta end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses c o s theta minus c o s squared theta close parentheses plus open parentheses s i n theta minus s i n squared theta close parentheses over denominator begin display style s i n theta c o s theta end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses c o s theta minus c o s squared theta plus s i n theta minus s i n squared theta close parentheses over denominator begin display style s i n theta c o s theta end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator open parentheses c o s theta plus s i n theta minus 1 close parentheses over denominator begin display style s i n theta c o s theta end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator c o s theta over denominator begin display style s i n theta c o s theta end style end fraction plus fraction numerator s i n theta over denominator begin display style s i n theta c o s theta end style end fraction minus fraction numerator 1 over denominator begin display style s i n theta c o s theta end style end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals cos e c theta plus s e c theta minus s e c theta cos e c theta

Answered by Vimala Ramamurthy | 29th Sep, 2015, 09:28: AM

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