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Asked by divya Vedula | 7th Jun, 2016, 10:58: AM

Expert Answer:

C o n s i d e r space t h e space L e f t space h a n d space s i d e space o f space t h e space e q u a t i o n comma space w e space h a v e comma
fraction numerator open parentheses tan theta plus s e c theta minus 1 close parentheses over denominator open parentheses tan theta minus s e c theta plus 1 close parentheses end fraction equals fraction numerator open parentheses begin display style fraction numerator sin theta over denominator cos theta end fraction end style plus fraction numerator 1 over denominator c o s theta end fraction minus 1 close parentheses over denominator open parentheses fraction numerator s i n theta over denominator c o s theta end fraction minus fraction numerator 1 over denominator c o s theta end fraction plus 1 close parentheses 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 equals fraction numerator open parentheses begin display style fraction numerator s i n theta plus 1 minus cos theta over denominator c o s theta end fraction end style close parentheses over denominator open parentheses fraction numerator s i n theta minus 1 plus c o s theta over denominator c o s theta end fraction close parentheses 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 equals fraction numerator s i n theta plus 1 minus c o s theta over denominator s i n theta minus 1 plus c o s 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 equals fraction numerator s i n theta minus open parentheses cos theta minus 1 close parentheses over denominator s i n theta plus open parentheses c o s theta minus 1 close parentheses 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 equals fraction numerator s i n theta minus open parentheses c o s theta minus 1 close parentheses over denominator s i n theta plus open parentheses c o s theta minus 1 close parentheses end fraction cross times fraction numerator s i n theta minus open parentheses c o s theta minus 1 close parentheses over denominator s i n theta minus open parentheses c o s theta minus 1 close parentheses 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 equals fraction numerator open square brackets sin theta minus open parentheses cos theta minus 1 close parentheses close square brackets squared over denominator s i n squared theta minus open parentheses c o s theta minus 1 close parentheses squared 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 equals fraction numerator open square brackets s i n squared theta plus open parentheses c o s theta minus 1 close parentheses squared minus 2 sin theta open parentheses c o s theta minus 1 close parentheses close square brackets over denominator s i n squared theta minus cos squared theta minus 1 plus 2 cos 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 equals fraction numerator open square brackets s i n squared theta plus c o s squared theta plus 1 minus 2 c o s theta minus 2 s i n theta cos theta plus 2 sin theta close square brackets over denominator negative 2 c o s squared theta plus 2 c o s 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 equals fraction numerator 2 minus 2 c o s theta minus 2 s i n theta c o s theta plus 2 s i n theta over denominator negative 2 c o s squared theta plus 2 c o s 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 equals fraction numerator 1 minus c o s theta minus s i n theta c o s theta plus s i n theta over denominator negative c o s squared theta plus c o s 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 equals fraction numerator 1 minus c o s theta minus s i n theta open parentheses cos theta minus 1 close parentheses over denominator negative c o s squared theta plus c o s 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 equals fraction numerator 1 minus c o s theta plus s i n theta open parentheses 1 minus c o s theta close parentheses over denominator cos theta open parentheses 1 minus cos theta close parentheses 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 equals fraction numerator open parentheses 1 minus cos theta close parentheses open parentheses 1 plus sin theta close parentheses over denominator c o s theta open parentheses 1 minus c o s theta close parentheses 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 equals fraction numerator open parentheses 1 plus s i n theta close parentheses over denominator c o s theta end fraction

Answered by Vimala | 8th Jun, 2016, 09:03: AM