tantheta/(1-costheta) + cottheta/(1-tantheta) = 1 + tantheta + cottheta

Asked by Sthitaprajna Mishra | 7th Sep, 2014, 03:47: PM

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 g i v e n space e q u a t i o n : fraction numerator tan theta over denominator 1 minus c o t theta end fraction plus fraction numerator c o t theta over denominator 1 minus tan theta end fraction equals fraction numerator tan theta open parentheses 1 minus tan theta close parentheses plus c o t theta open parentheses 1 minus c o t theta close parentheses over denominator open parentheses 1 minus c o t theta close parentheses open parentheses 1 minus tan 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 space space space space space space equals fraction numerator tan theta open parentheses 1 minus tan theta close parentheses plus c o t theta open parentheses 1 minus c o t theta close parentheses over denominator open parentheses 1 minus c o t theta close parentheses open parentheses 1 minus tan 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 space space space space space space equals fraction numerator tan theta minus tan squared theta plus c o t theta minus c o t squared theta over denominator 1 minus tan theta minus c o t theta plus 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 equals fraction numerator open parentheses 2 minus tan theta minus c o t theta close parentheses open parentheses 1 plus tan theta plus c o t theta close parentheses over denominator 2 minus tan theta minus 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 equals 1 plus tan theta plus c o t theta

Answered by Vimala Ramamurthy | 8th Sep, 2014, 09:25: AM

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