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Pertanyaan

Jika sin x + cos y = 3 1 ​ d an cos x + sin y = 3 2 ​ maka sin ( x + y) = ....

Jika   maka sin (x + y) =  ....

  1. begin mathsize 14px style negative 23 over 18 end style 

  2. begin mathsize 14px style negative 13 over 18 end style 

  3. begin mathsize 14px style negative 13 over 9 end style 

  4. begin mathsize 14px style 13 over 18 end style 

  5. begin mathsize 14px style 23 over 18 end style 

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R. Fajar

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.

Pembahasan

Perhatikan bahwa dan Dari persamaan (1) dan (2), didapatkan Ingat bahwa .Sehingga Jadi, jawaban yang tepat adalah B.

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application x plus cos invisible function application y end cell equals cell 1 third end cell row cell open parentheses sin invisible function application x plus cos invisible function application y close parentheses squared end cell equals cell open parentheses 1 third close parentheses squared end cell row cell sin squared invisible function application x plus 2 sin invisible function application x cos invisible function application y plus cos squared invisible function application y end cell equals cell 1 over 9 horizontal ellipsis open parentheses 1 close parentheses end cell end table end style 

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application x plus sin invisible function application y end cell equals cell 2 over 3 end cell row cell open parentheses cos invisible function application x plus sin invisible function application y close parentheses squared end cell equals cell open parentheses 2 over 3 close parentheses squared end cell row cell cos squared invisible function application x plus 2 cos invisible function application x sin invisible function application y plus sin squared invisible function application y end cell equals cell 4 over 9 horizontal ellipsis open parentheses 2 close parentheses end cell end table end style 

Dari persamaan (1) dan (2), didapatkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses sin squared invisible function application x plus 2 sin invisible function application x cos invisible function application y plus cos squared invisible function application y close parentheses plus open parentheses cos squared invisible function application x plus 2 cos invisible function application x sin invisible function application y plus sin squared invisible function application y close parentheses end cell equals cell 1 over 9 plus 4 over 9 end cell row cell sin squared invisible function application x plus cos squared invisible function application x plus 2 sin invisible function application x cos invisible function application y plus 2 cos invisible function application x sin invisible function application y plus cos squared invisible function application y plus sin squared invisible function application y end cell equals cell 5 over 9 end cell row cell open parentheses sin squared invisible function application x plus cos squared invisible function application x close parentheses plus 2 open parentheses sin invisible function application x cos invisible function application y plus cos invisible function application x sin invisible function application y close parentheses plus open parentheses sin squared invisible function application y plus cos squared invisible function application y close parentheses end cell equals cell 5 over 9 end cell end table end style 

Ingat bahwa begin mathsize 14px style sin squared invisible function application A plus cos squared invisible function application A equals 1 space d a n space sin invisible function application A cos invisible function application B plus cos invisible function application A sin invisible function application B equals sin invisible function application open parentheses A plus B close parentheses end style. Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses sin squared invisible function application x plus cos squared invisible function application x close parentheses plus 2 open parentheses sin invisible function application x cos invisible function application y plus cos invisible function application x sin invisible function application y close parentheses plus open parentheses sin squared invisible function application y plus cos squared invisible function application y close parentheses end cell equals cell 5 over 9 end cell row cell 1 plus 2 sin invisible function application open parentheses x plus y close parentheses plus 1 end cell equals cell 5 over 9 end cell row cell 2 plus 2 sin invisible function application open parentheses x plus y close parentheses end cell equals cell 5 over 9 end cell row cell 2 sin invisible function application open parentheses x plus y close parentheses end cell equals cell 5 over 9 minus 2 end cell row cell 2 sin invisible function application open parentheses x plus y close parentheses end cell equals cell 5 over 9 minus 18 over 9 end cell row cell 2 sin invisible function application open parentheses x plus y close parentheses end cell equals cell negative 13 over 9 end cell row cell sin invisible function application open parentheses x plus y close parentheses end cell equals cell negative 13 over 18 end cell end table end style 

Jadi, jawaban yang tepat adalah B.

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