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Hasil dari tan165∘+tan75∘tan52,5∘−tan7,5∘​ adalah ...

Pertanyaan

Hasil dari begin mathsize 14px style fraction numerator tan space 52 comma 5 degree minus tan space 7 comma 5 degree over denominator tan space 165 degree plus tan space 75 degree end fraction end style adalah ...

  1. begin mathsize 14px style 1 third open parentheses 2 square root of 3 minus square root of 6 close parentheses end style 

  2. begin mathsize 14px style 1 third open parentheses 2 square root of 3 plus square root of 6 close parentheses end style 

  3. begin mathsize 14px style 1 third open parentheses square root of 3 minus square root of 6 close parentheses end style 

  4. begin mathsize 14px style 1 half open parentheses 2 square root of 3 minus square root of 6 close parentheses end style 

  5. begin mathsize 14px style 1 half open parentheses 2 square root of 3 plus square root of 6 close parentheses end style 

Pembahasan Video:

Pembahasan Soal:

Ingat: sin space open parentheses A plus-or-minus B close parentheses equals sin space A space cos space B space plus-or-minus space cos space A space sin space B 

          cos space A space cos space B equals 1 half cos space open parentheses A plus B close parentheses plus 1 half cos space open parentheses A minus B close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space 52 comma 5 degree minus tan space 7 comma 5 degree over denominator tan space 165 degree plus tan space 75 degree end fraction end cell equals cell fraction numerator begin display style fraction numerator sin space 52 comma 5 degree over denominator cos space 52 comma 5 degree end fraction end style minus begin display style fraction numerator sin space 7 comma 5 degree over denominator cos space 7 comma 5 degree end fraction end style over denominator begin display style fraction numerator sin space 165 degree over denominator cos space 165 degree end fraction end style plus begin display style fraction numerator sin space 75 degree over denominator cos space 75 degree end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator sin space 52 comma 5 degree space cos space 7 comma 5 degree minus cos space 52 comma 5 degree sin space 7 comma 5 degree over denominator cos space 52 comma 5 degree space cos space 7 comma 5 degree end fraction end style over denominator begin display style fraction numerator sin space 165 degree space cos space 75 degree plus cos space 165 degree sin space 75 degree over denominator cos space 165 degree cos space 75 degree end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator sin space open parentheses 52 comma 5 degree minus 7 comma 5 degree close parentheses over denominator begin display style 1 half end style cos space open parentheses 52 comma 5 degree plus 7 comma 5 degree close parentheses plus begin display style 1 half end style cos space open parentheses 52 comma 5 degree minus 7 comma 5 degree close parentheses end fraction end style over denominator begin display style fraction numerator sin space open parentheses 165 degree plus 75 degree close parentheses over denominator 1 half cos space open parentheses 165 degree plus 75 degree close parentheses plus 1 half cos space open parentheses 165 degree minus 75 degree close parentheses end fraction end style end fraction cross times fraction numerator begin display style 1 half end style over denominator begin display style 1 half end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator sin space 45 degree over denominator cos space 60 degree plus cos space 45 degree end fraction end style space over denominator begin display style fraction numerator sin space 240 degree over denominator cos space 240 degree plus cos space 90 degree end fraction end style end fraction end cell end table

Dengan sudut berelasi

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 240 degree end cell equals cell sin space open parentheses 180 degree plus 60 degree close parentheses end cell row blank equals cell negative sin space 60 degree end cell row blank equals cell negative 1 half square root of 3 end cell end table

dan 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 240 degree end cell equals cell cos space open parentheses 180 degree plus 60 degree close parentheses end cell row blank equals cell negative cos space 60 degree end cell row blank equals cell negative 1 half end cell end table

maka menjadi

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space 52 comma 5 degree minus tan space 7 comma 5 degree over denominator tan space 165 degree plus tan space 75 degree end fraction end cell equals cell fraction numerator begin display style 1 half end style square root of 2 over denominator begin display style 1 half end style plus begin display style 1 half end style square root of 2 end fraction cross times fraction numerator negative begin display style 1 half end style plus 0 over denominator negative begin display style 1 half end style square root of 3 end fraction cross times 4 over 4 end cell row blank equals cell fraction numerator square root of 2 over denominator square root of 6 minus square root of 3 end fraction cross times fraction numerator square root of 6 minus square root of 3 over denominator square root of 6 minus square root of 3 end fraction end cell row blank equals cell fraction numerator 2 square root of 3 minus square root of 6 over denominator 6 minus 3 end fraction end cell row blank equals cell 1 third open parentheses 2 square root of 3 minus square root of 6 close parentheses end cell end table

Jadi, jawaban yang tepat adalah A

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Terakhir diupdate 06 Oktober 2021

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