Tan square A/tan square A-1+Cosec square A/sec square A-Cosec square A=1/1-2 cos square A

Asked by bindu_jayk | 15th Aug, 2019, 11:45: AM

Expert Answer:

begin mathsize 16px style fraction numerator tan squared straight A over denominator tan squared straight A space minus space 1 end fraction space plus space fraction numerator cos begin display style begin display style ec end style squared end style begin display style straight A end style over denominator sec squared straight A space minus space cosec squared straight A end fraction space equals space fraction numerator 1 over denominator 1 space minus space 2 cos squared straight A end fraction
straight L. straight H. straight S space equals space fraction numerator begin display style tan squared straight A end style over denominator begin display style tan squared straight A space minus space 1 end style end fraction space plus space fraction numerator begin display style cos ec squared straight A end style over denominator sec squared straight A space minus space cosec squared straight A end fraction
space space space space space space space space space space space equals fraction numerator begin display style fraction numerator begin display style sin squared end style begin display style straight A end style over denominator begin display style cos squared end style begin display style straight A end style end fraction end style over denominator fraction numerator begin display style sin squared straight A end style over denominator begin display style cos squared straight A space end style end fraction begin display style minus end style begin display style space end style begin display style 1 end style end fraction space plus space fraction numerator begin display style fraction numerator 1 over denominator begin display style sin squared end style begin display style straight A end style end fraction end style over denominator begin display style fraction numerator 1 over denominator begin display style cos squared end style begin display style straight A end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style sin squared straight A end style end fraction space end style end fraction
space space space space space space space space space space equals space fraction numerator begin display style sin squared end style begin display style straight A end style over denominator sin squared straight A space minus space cos squared straight A end fraction plus space fraction numerator begin display style cos squared straight A end style over denominator sin squared straight A space minus space cos squared straight A end fraction
space space space space space space space space space space equals space fraction numerator sin squared straight A plus cos squared straight A over denominator 1 minus space cos squared straight A space minus space cos squared straight A end fraction
space space space space space space space space space space equals fraction numerator 1 over denominator 1 space minus space 2 cos squared straight A end fraction
space space space space space space space space space space equals straight R. straight H. straight S
Hence space proved. end style

Answered by Yasmeen Khan | 16th Aug, 2019, 10:46: AM