Pls solve

Asked by pb_ckt | 11th Jun, 2019, 03:33: PM

Expert Answer:

let space straight theta equals straight a plus straight b
given space that space space straight phi space equals straight a minus straight b
also
tan space straight a space equals space straight k space tan space straight b
fraction numerator tan space straight a over denominator tan space straight b end fraction space equals space straight k
by space componendo space and space dividendo
fraction numerator tan space straight a space minus space tan space straight b over denominator tan space straight a space plus space tan space straight b end fraction equals fraction numerator straight k minus 1 over denominator straight k plus 1 end fraction
fraction numerator begin display style fraction numerator sin space straight a over denominator cos space straight a end fraction end style minus begin display style fraction numerator sin space straight b over denominator cos space straight b end fraction end style over denominator fraction numerator sin space straight a over denominator cos space straight a end fraction plus fraction numerator sin space straight b over denominator cos space straight b end fraction end fraction equals fraction numerator straight k minus 1 over denominator straight k plus 1 end fraction
fraction numerator begin display style sin space straight a space cos space straight b minus sin space straight b space cos space straight a end style over denominator sin space straight a space cos space straight b plus sin space straight b space cos space straight a end fraction equals fraction numerator straight k minus 1 over denominator straight k plus 1 end fraction
fraction numerator begin display style sin space open parentheses straight a minus straight b close parentheses end style over denominator sin space left parenthesis straight a plus straight b right parenthesis end fraction equals fraction numerator straight k minus 1 over denominator straight k plus 1 end fraction
fraction numerator begin display style sin space straight phi end style over denominator sin space straight theta end fraction equals fraction numerator straight k minus 1 over denominator straight k plus 1 end fraction

Answered by Arun | 13th Jun, 2019, 10:15: AM