root sec thita  -  1 / sec thita  + 1 =  root   sec  thita  +1-  sec thita -  1  =  2 cosec  thita

Asked by abhinav | 11th Jun, 2017, 05:50: PM

Expert Answer:

begin mathsize 16px style straight L. straight H. straight S. equals square root of fraction numerator sec space straight theta minus 1 over denominator sec space plus 1 end fraction end root plus square root of fraction numerator sec space straight theta plus 1 over denominator sec space straight theta minus 1 end fraction end root
equals square root of fraction numerator begin display style fraction numerator 1 over denominator cos space straight theta end fraction end style minus 1 over denominator fraction numerator 1 over denominator cos space straight theta end fraction plus 1 end fraction end root plus square root of fraction numerator begin display style fraction numerator 1 over denominator cos space straight theta end fraction plus 1 end style over denominator fraction numerator 1 over denominator cos space straight theta end fraction minus 1 end fraction end root
equals square root of fraction numerator begin display style fraction numerator 1 minus cos space straight theta over denominator cos space straight theta end fraction end style over denominator begin display style fraction numerator 1 plus cos space straight theta over denominator cos space straight theta end fraction end style end fraction end root plus square root of fraction numerator begin display style fraction numerator 1 plus cos space straight theta over denominator cos space straight theta end fraction end style over denominator begin display style fraction numerator 1 minus cos space straight theta over denominator cos space straight theta end fraction end style end fraction end root
equals square root of fraction numerator 1 minus cos space straight theta over denominator 1 plus cos space straight theta end fraction end root plus square root of fraction numerator 1 plus cos space straight theta over denominator 1 minus cos space straight theta end fraction end root
equals square root of fraction numerator left parenthesis 1 minus cos space straight theta right parenthesis left parenthesis 1 minus cos space straight theta right parenthesis over denominator left parenthesis 1 plus cos space straight theta right parenthesis left parenthesis 1 minus cos space straight theta right parenthesis end fraction end root plus square root of fraction numerator left parenthesis 1 plus cos space straight theta right parenthesis left parenthesis 1 plus cos space straight theta right parenthesis over denominator left parenthesis 1 minus cos space straight theta right parenthesis left parenthesis 1 plus cos space straight theta right parenthesis end fraction end root
equals square root of fraction numerator open parentheses 1 minus cos space straight theta close parentheses squared over denominator 1 minus cos squared straight theta end fraction end root plus square root of fraction numerator open parentheses 1 plus cos space straight theta close parentheses squared over denominator 1 minus cos squared straight theta end fraction end root
equals square root of fraction numerator open parentheses 1 minus cos space straight theta close parentheses squared over denominator sin squared straight theta end fraction end root plus square root of fraction numerator open parentheses 1 plus cos space straight theta close parentheses squared over denominator sin squared straight theta end fraction end root
equals fraction numerator open parentheses 1 minus cos space straight theta close parentheses over denominator sin space straight theta end fraction plus fraction numerator open parentheses 1 plus cos space straight theta close parentheses over denominator sin space straight theta end fraction
equals fraction numerator 1 minus cosθ plus 1 plus cosθ over denominator sin space straight theta end fraction
equals fraction numerator 2 over denominator sin space straight theta end fraction
equals 2 space cosec space straight theta
equals straight R. straight H. straight S. end style

Answered by Rashmi Khot | 11th Jun, 2017, 07:41: PM