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Pertanyaan

Diketahui sin open parentheses x close parentheses plus sin open parentheses y close parentheses equals 1 half space dan space italic cos begin italic style left parenthesis x right parenthesis end style plus cos open parentheses straight y close parentheses equals 1 third dengan x space dan space y sudut lancip. Hitunglah:

cos open parentheses x minus y close parentheses 

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

diperoleh cos open parentheses x minus y close parentheses equals negative 59 over 72.

Pembahasan

Diketahui sin open parentheses x close parentheses plus sin open parentheses y close parentheses equals 1 half space dan space italic cos begin italic style left parenthesis x right parenthesis end style plus cos open parentheses straight y close parentheses equals 1 third, akan dibuktikan cos open parentheses x minus y close parentheses

Ingat bahwa

cos open parentheses x minus y close parentheses equals cos space x space cos space y space plus sin space x space sin space y sin squared x plus cos squared x equals 1  

Diperoleh perhitungan

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses sin open parentheses x close parentheses plus sin open parentheses y close parentheses close parentheses squared plus open parentheses italic cos italic left parenthesis x italic right parenthesis plus cos open parentheses straight y close parentheses close parentheses squared end cell equals cell open parentheses 1 half close parentheses squared plus open parentheses 1 third close parentheses squared end cell row cell sin squared x plus 2 sin x space sin y plus sin squared y plus cos squared x plus 2 cos x space cos y plus cos squared y end cell equals cell 1 fourth plus 1 over 9 end cell row cell open parentheses sin squared x plus co s squared x close parentheses plus 2 sin x space sin y plus 2 cos x space cos y plus open parentheses sin squared y plus cos squared y close parentheses end cell equals cell 13 over 36 end cell row cell 1 plus 2 sin x space sin y plus 2 cos x space cos y plus 1 end cell equals cell 13 over 36 end cell row cell 2 left parenthesis sin space x space sin space y plus cos space x space cos space y right parenthesis end cell equals cell 13 over 36 minus 2 end cell row cell 2 left parenthesis sin space x space sin space y plus cos space x space cos space y right parenthesis end cell equals cell negative 59 over 36 end cell row cell sin space x space sin space y plus cos space x space cos space y end cell equals cell negative 59 over 72 end cell row cell cos left parenthesis x minus y right parenthesis end cell equals cell negative 59 over 72 end cell end table end style 

Dengan demikian, diperoleh cos open parentheses x minus y close parentheses equals negative 59 over 72.

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