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Buktikan identitas berikut. b. cos 5 θ ⋅ sin θ + cos θ ⋅ sin 3 θ − cos 2 θ ⋅ sin 4 θ = 0

Buktikan identitas berikut.

b.  

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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terbukti bahwa .

terbukti bahwa cos space 5 straight theta times sin space straight theta plus cos space straight theta times sin space 3 straight theta minus cos space 2 straight theta times sin space 4 straight theta equals 0.

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

Ingat kembali:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space cos space straight alpha space sin space straight beta end cell equals cell sin space open parentheses straight alpha plus straight beta close parentheses minus sin space open parentheses straight alpha minus straight beta close parentheses end cell end table 

Akan dibuktikan cos space 5 straight theta times sin space straight theta plus cos space straight theta times sin space 3 straight theta minus cos space 2 straight theta times sin space 4 straight theta equals 0. Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell cos space 5 straight theta times sin space straight theta plus cos space straight theta times sin space 3 straight theta minus cos space 2 straight theta times sin space 4 straight theta end cell row blank equals cell open parentheses sin space open parentheses 5 straight theta plus straight theta close parentheses minus sin space open parentheses 5 straight theta minus straight theta close parentheses close parentheses plus open parentheses sin space open parentheses straight theta plus 3 straight theta close parentheses minus sin space open parentheses straight theta minus 3 straight theta close parentheses close parentheses minus open parentheses sin space open parentheses 2 straight theta plus 4 straight theta close parentheses minus sin space open parentheses 2 straight theta minus 4 straight theta close parentheses close parentheses end cell row blank equals cell open parentheses sin space 6 straight theta minus sin space 4 straight theta close parentheses plus open parentheses sin space 4 straight theta minus sin space open parentheses negative 2 straight theta close parentheses close parentheses minus open parentheses sin space 6 straight theta minus sin space open parentheses negative 2 straight theta close parentheses close parentheses end cell row blank equals cell open parentheses sin space 6 straight theta minus sin space 4 straight theta close parentheses plus open parentheses sin space 4 straight theta plus sin space 2 straight theta close parentheses minus open parentheses sin space 6 straight theta plus sin space 2 straight theta close parentheses end cell row blank equals cell sin space 6 straight theta minus sin space 4 straight theta plus sin space 4 straight theta plus sin space 2 straight theta minus sin space 6 straight theta minus sin space 2 straight theta end cell row blank equals cell up diagonal strike sin space 6 straight theta end strike up diagonal strike negative sin space 6 straight theta end strike up diagonal strike negative sin space 4 straight theta end strike up diagonal strike plus sin space 4 straight theta end strike up diagonal strike plus sin space 2 straight theta end strike up diagonal strike negative sin space 2 straight theta end strike end cell row blank equals 0 end table end style  

Jadi, terbukti bahwa cos space 5 straight theta times sin space straight theta plus cos space straight theta times sin space 3 straight theta minus cos space 2 straight theta times sin space 4 straight theta equals 0.

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