Sir in exercise 21(E)
 
Question -1, part xiii
 
Is there any alternative method to do this part other than the given answer ?

Asked by Yatin | 19th Jul, 2017, 03:05: PM

Expert Answer:

begin mathsize 16px style You space can space solve space by space following space method space also.
straight L. straight H. straight S. equals fraction numerator left parenthesis cosecA minus cotA right parenthesis squared plus 1 over denominator secA left parenthesis cosecA minus cotA right parenthesis end fraction
equals fraction numerator open parentheses begin display style 1 over sinA end style minus begin display style cosA over sinA end style close parentheses squared plus 1 over denominator begin display style 1 over cosA end style open parentheses 1 over sinA minus cosA over sinA close parentheses end fraction
equals fraction numerator open parentheses begin display style fraction numerator 1 minus cosA over denominator sinA end fraction end style close parentheses squared plus 1 over denominator begin display style 1 over cosA open parentheses fraction numerator 1 minus cosA over denominator sinA end fraction close parentheses end style end fraction
equals fraction numerator begin display style fraction numerator left parenthesis 1 minus cosA right parenthesis over denominator sin squared straight A end fraction end style squared plus 1 over denominator begin display style fraction numerator 1 minus cosA over denominator sinA space cosA end fraction end style end fraction
equals fraction numerator begin display style fraction numerator 1 plus cos squared straight A minus 2 cosA plus sin squared straight A over denominator sin squared straight A end fraction end style over denominator begin display style fraction numerator 1 minus cosA over denominator sinA space cosA end fraction end style end fraction
equals fraction numerator begin display style fraction numerator 1 plus 1 minus 2 cosA over denominator sin squared straight A end fraction end style over denominator begin display style fraction numerator 1 minus cosA over denominator sinA space cosA end fraction end style end fraction
equals fraction numerator 2 minus 2 cosA over denominator sin squared straight A end fraction cross times fraction numerator sinA space cosA over denominator 1 minus cosA end fraction
equals fraction numerator 2 left parenthesis 1 minus cosA right parenthesis over denominator sinA end fraction cross times fraction numerator cosA over denominator 1 minus cosA end fraction
equals 2 cross times cosA over sinA
equals 2 cotA
equals straight R. straight H. straight S. end style

Answered by Rashmi Khot | 19th Jul, 2017, 03:56: PM