Pertanyaan

(SBMPTN 2015) Jika cos ( x + 1 5 ∘ ) = a dengan 0 ∘ ≤ x ≤ 3 0 ∘ , maka nilai cos ( 2 x + 6 0 ∘ ) adalah...

(SBMPTN 2015)

Jika $cos (x + 1 5^{\circ}) = a$ dengan $0^{\circ} \leq x \leq 3 0^{\circ}$ , maka nilai $cos (2 x + 6 0^{\circ})$ adalah...

$fraction numerator square root of 3 over denominator 2 end fraction open parentheses 2 a squared minus 1 close parentheses plus a square root of 1 minus a squared end root$
$fraction numerator square root of 3 over denominator 2 end fraction open parentheses 2 a squared minus 1 close parentheses minus a square root of 1 minus a squared end root$
$fraction numerator square root of 3 over denominator 2 end fraction open parentheses a squared plus 1 close parentheses minus a square root of 1 minus a squared end root$
$fraction numerator square root of 3 over denominator 2 end fraction open parentheses 2 a squared minus 1 close parentheses minus a square root of 1 plus a squared end root$
$fraction numerator square root of 3 over denominator 2 end fraction open parentheses a squared minus 1 close parentheses plus a square root of 1 minus a squared end root$

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Habis dalam

Klaim

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Ingat! Sudut rangkap: Penjumlahan sudut: Diketahui : , kita dapat menggunakan bantuan segitiga siku-siku untuk mengetahui nilai sinus sudut tersebut,yaitu : Jadi,

Ingat!

Sudut rangkap:

Penjumlahan sudut:

Diketahui :

, kita dapat menggunakan bantuan segitiga siku-siku untuk mengetahui nilai sinus sudut tersebut, yaitu :

Jadi,

$cos space open parentheses 2 x plus 60 degree close parentheses equals cos space open parentheses 2 open parentheses x plus 15 degree close parentheses plus 30 degree close parentheses equals cos space open parentheses 2 open parentheses x plus 15 degree close parentheses close parentheses. co s space 30 degree minus sin space open parentheses 2 open parentheses x plus 15 degree close parentheses close parentheses. sin space 30 degree equals open parentheses 2 cos squared space open parentheses x plus 15 degree close parentheses minus 1 close parentheses. cos space 30 degree minus 2 sin space open parentheses x plus 15 degree close parentheses cos space open parentheses x plus 15 degree close parentheses. sin space 30 degree equals open parentheses 2 open parentheses a squared close parentheses minus 1 close parentheses.1 half square root of 3 minus 2. square root of 1 minus a squared end root. a.1 half equals fraction numerator square root of 3 over denominator 2 end fraction open parentheses 2 a squared minus 1 close parentheses minus a square root of 1 minus a squared end root$