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Buktikan: b. 4 sin 1 8 ∘ cos 3 6 ∘ sin 5 4 ∘ = 1 + 2 sin 1 8 ∘ − cos 3 6 ∘

Buktikan:

b.  

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S. Nur

Master Teacher

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terbukti bahwa .

terbukti bahwa 4 space sin space 18 degree space cos space 36 degree space sin space 54 degree equals 1 plus 2 space sin space 18 degree minus cos space 36 degree.

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

Ingat kembali:

2 space sin space straight alpha space cos space straight beta equals sin space open parentheses straight alpha plus straight beta close parentheses plus sin space open parentheses straight alpha minus straight beta close parentheses sin space open parentheses 90 degree minus straight A close parentheses equals cos space straight A 

Akan dibuktikan 4 space sin space 18 degree space cos space 36 degree space sin space 54 degree equals 1 plus 2 space sin space 18 degree minus cos space 36 degree. Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell 4 space sin space 18 degree space cos space 36 degree space sin space 54 degree end cell row blank equals cell 2 times 2 times sin space 18 degree space cos space 36 degree space sin space open parentheses 90 degree minus 36 degree close parentheses end cell row blank equals cell 2 times 2 times sin space 18 degree space cos space 36 degree space cos space 36 degree end cell row blank equals cell 2 times open parentheses 2 times sin space 18 degree space cos space 36 degree close parentheses space cos space 36 degree end cell row blank equals cell 2 times open square brackets sin space open parentheses 18 degree plus 36 degree close parentheses plus sin space open parentheses 18 degree minus 36 degree close parentheses close square brackets space cos space 36 degree end cell row blank equals cell 2 times open parentheses sin space 54 degree plus sin space open parentheses negative 18 degree close parentheses close parentheses space cos space 36 degree end cell row blank equals cell 2 times open parentheses sin space 54 degree minus sin space 18 degree close parentheses space cos space 36 degree end cell row blank equals cell 2 space sin space 54 degree space cos space 36 degree minus 2 space sin space 18 degree space cos space 36 degree end cell row blank equals cell open square brackets sin space open parentheses 54 degree plus 36 degree close parentheses plus sin space open parentheses 54 degree minus 36 degree close parentheses close square brackets minus open square brackets sin space open parentheses 18 degree plus 36 degree close parentheses plus sin space open parentheses 18 degree minus 36 degree close parentheses close square brackets end cell row blank equals cell open parentheses sin space 90 degree plus sin space 18 degree close parentheses minus open parentheses sin space 54 degree plus sin space open parentheses negative 18 degree close parentheses close parentheses end cell row blank equals cell open parentheses 1 plus sin space 18 degree close parentheses minus open parentheses sin space 54 degree minus sin space 18 degree close parentheses end cell row blank equals cell 1 plus sin space 18 degree minus sin space 54 degree plus sin space 18 degree end cell row blank equals cell 1 plus 2 space sin space 18 degree minus sin space 54 degree end cell row blank equals cell 1 plus 2 space sin space 18 degree minus sin space open parentheses 90 degree minus 36 degree close parentheses end cell row blank equals cell 1 plus 2 space sin space 18 degree minus cos space 36 degree end cell end table end style  

Jadi, terbukti bahwa 4 space sin space 18 degree space cos space 36 degree space sin space 54 degree equals 1 plus 2 space sin space 18 degree minus cos space 36 degree.

Latihan Bab

Konsep Kilat

Jumlah dan Selisih Dua Sudut

Sudut Rangkap dan Sudut Paruh

Perkalian Trigonometri

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Tentukan nilai dari: sin 3 5 ∘ cos 5 ∘ − cos 3 5 ∘ cos 8 5 ∘ .

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