<prompt> Tafuta thamani ya cotcot-13cot-17cot-113cot-121.  <response>: Ninagundua kuwa hoja ya chaguo za kukokotoa za kotanjenti ni jumla ya vitendakazi vinne kinyume vya kotanjenti. Nakumbuka kwamba kuna fomula ya kotangent kinyume ya jumla ya nambari mbili: cot-1xcot-1y cot-1 leftfracxy-1xyright. Ninashangaa ikiwa ninaweza kutumia fomula hii kurahisisha hoja ya kitendakazi cha cotangent. Ninaanza kwa kupanga maneno mawili ya kwanza na maneno mawili ya mwisho: cotcot-13cot-17cot-113cot -121 kitandakushotokitanda-13kitanda-17kitanda-113kitanda-121 kulia. Ninatumia fomula kwa kila jozi ya maneno: cotleftcot-13cot-17cot-1 13kitanda-121kulia kitandakushotokitanda-1kushotofrac3cdot 7-137kulia cot-1leftfrac13cdot 21-11321kuliakulia. Ninarahisisha visehemu vilivyo ndani ya vitendakazi kinyume vya kotangent: cotleft cot-1leftfrac3cdot 7-137rightcot-1leftfrac13cdot 21-1 1321kuliakulia cotkushotocot-1leftfrac2010kuliacot-1left frac27234kuliakulia. Ninapunguza sehemu hadi masharti ya chini kabisa: cotleftcot-1leftfrac2010 kuliacot-1leftfrac27234rightright cotleftcot-12cot-1 8kulia. Ninatumia fomula tena kwa maneno mawili yaliyosalia: cotleftcot-12cot-18 kulia cotleftcot-1leftfrac2cdot 8-128rightright. Ninarahisisha sehemu ndani ya cotangent inverse kazi: cotleftcot-1leftfrac2cdot 8-128rightright cotleftcot -1kushotofrac1510kuliakulia. Ninapunguza sehemu hadi masharti ya chini kabisa: cotleftcot-1leftfrac 1510kuliakulia cotleftcot-1leftfrac32kuliakulia. Ninaona kwamba cotangent na vitendaji tofauti vya kukokotoa vinaghairi, na kuniacha na hoja: cotleftcot-1leftfrac32rightright frac3 2. 