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Buktikan: 2 sin 3 x sin 4 x + 2 cos 5 x cos 2 x − cos 3 x = cos x

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

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terbukti bahwa .

terbukti bahwa 2 space sin space 3 x space sin space 4 x plus 2 space cos space 5 x space cos space 2 x minus cos space 3 x equals cos space x.

Pembahasan

Ingat kembali: Akan dibuktikan . Maka: Jadi, terbukti bahwa .

Ingat kembali:

2 space cos space straight alpha space cos space straight beta equals cos space open parentheses straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha minus straight beta close parentheses 2 space sin space straight alpha space sin space straight beta equals negative cos space open parentheses straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha minus straight beta close parentheses 

Akan dibuktikan 2 space sin space 3 x space sin space 4 x plus 2 space cos space 5 x space cos space 2 x minus cos space 3 x equals cos space x. Maka:

  begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell 2 space sin space 3 x space sin space 4 x plus 2 space cos space 5 x space cos space 2 x minus cos space 3 x end cell row blank equals cell open square brackets cos space open parentheses 3 x plus 4 x close parentheses plus cos space open parentheses 3 x minus 4 x close parentheses close square brackets plus open square brackets negative cos space open parentheses 5 x plus 2 x close parentheses plus cos space open parentheses 5 x minus 2 x close parentheses close square brackets minus cos space 3 x end cell row blank equals cell open parentheses cos space 7 x plus cos space open parentheses negative x close parentheses close parentheses plus open parentheses negative cos space 7 x plus cos space 3 x close parentheses minus cos space 3 x end cell row blank equals cell open parentheses cos space 7 x plus cos space x close parentheses plus open parentheses negative cos space 7 x plus cos space 3 x close parentheses minus cos space 3 x end cell row blank equals cell up diagonal strike cos space 7 x end strike plus cos space x up diagonal strike negative cos space 7 x end strike up diagonal strike plus cos space 3 x end strike up diagonal strike negative cos space 3 x end strike end cell row blank equals cell cos space x end cell end table end style 

Jadi, terbukti bahwa 2 space sin space 3 x space sin space 4 x plus 2 space cos space 5 x space cos space 2 x minus cos space 3 x equals cos space x.

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