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Tunjukkan bahwa 8 sin 2 0 ∘ ⋅ sin 4 0 ∘ ⋅ sin 8 0 ∘ = 3 ​ .

Tunjukkan bahwa .

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

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terbukti bahwa .

terbukti bahwa 8 space sin space 20 degree times sin space 40 degree times sin space 80 degree equals square root of 3.

Pembahasan

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

Ingat kembali:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin space straight alpha space sin space straight beta end cell equals cell negative cos space open parentheses straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha minus straight beta close parentheses end cell 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 8 space sin space 20 degree times sin space 40 degree times sin space 80 degree equals square root of 3. Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell 8 space sin space 20 degree times sin space 40 degree times sin space 80 degree end cell row blank equals cell 4 times 2 times sin space 20 degree times sin space 40 degree times sin space 80 degree end cell row blank equals cell open parentheses 4 space sin space 20 degree close parentheses open parentheses 2 times sin space 80 degree times sin space 40 degree close parentheses end cell row blank equals cell open parentheses 4 space sin space 20 degree close parentheses open parentheses negative cos space open parentheses 80 degree plus 40 degree close parentheses plus cos space open parentheses 80 degree minus 40 degree close parentheses close parentheses end cell row blank equals cell open parentheses 4 space sin space 20 degree close parentheses open parentheses negative cos space 120 degree plus cos space 40 degree close parentheses end cell row blank equals cell open parentheses 4 space sin space 20 degree close parentheses open parentheses negative open parentheses negative 1 half close parentheses plus cos space 40 degree close parentheses end cell row blank equals cell open parentheses 4 space sin space 20 degree close parentheses open parentheses 1 half plus cos space 40 degree close parentheses end cell row blank equals cell 2 space sin space 20 degree plus 4 times sin space 20 degree times cos space 40 degree end cell row blank equals cell 2 space sin space 20 degree plus 2 times 2 times sin space 20 degree times cos space 40 degree end cell row blank equals cell 2 space sin space 20 degree plus 2 times open parentheses 2 times cos space 40 degree times sin space 20 degree close parentheses end cell row blank equals cell 2 space sin space 20 degree plus 2 open parentheses sin space open parentheses 40 degree plus 20 degree close parentheses minus sin space open parentheses 40 degree minus 20 degree close parentheses close parentheses end cell row blank equals cell 2 space sin space 20 degree plus 2 open parentheses sin space 60 degree minus sin space 20 degree close parentheses end cell row blank equals cell 2 space sin space 20 degree plus 2 open parentheses 1 half square root of 3 minus sin space 20 degree close parentheses end cell row blank equals cell up diagonal strike 2 space sin space 20 degree end strike plus square root of 3 up diagonal strike negative 2 space sin space 20 degree end strike end cell row blank equals cell square root of 3 end cell end table end style 

Jadi, terbukti bahwa 8 space sin space 20 degree times sin space 40 degree times sin space 80 degree equals square root of 3.

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