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Pertanyaan

Jika sin(2x + 45°) = a dan sin(x + 30°) = b, maka cos(3x + 75°) cos(x + 15°) =  .... 

  1. begin mathsize 14px style 1 minus straight a squared plus straight b squared end style

  2. begin mathsize 14px style 1 minus straight a squared minus straight b squared end style

  3. begin mathsize 14px style straight a squared plus straight b squared minus 1 end style

  4. begin mathsize 14px style 2 minus straight a squared straight b squared end style

  5. begin mathsize 14px style 1 minus straight a squared straight b squared end style

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style box enclose Ingat space rumus space colon  space space cos invisible function application open parentheses straight a plus straight b close parentheses equals cos invisible function application space straight a space cos invisible function application space straight b minus sin invisible function application space straight a space sin space invisible function application straight b space space  space space cos invisible function application open parentheses straight a minus straight b close parentheses equals cos invisible function application space straight a space cos invisible function application space straight b plus sin invisible function application space straight a space sin invisible function application space straight b end enclose    Pertama space – space tama space lihat space terlebih space dahulu space bahwa space colon  sin invisible function application open parentheses 2 straight x plus 45 degree close parentheses equals straight a equals straight a over 1 end style

begin mathsize 14px style Maka comma space cos invisible function application open parentheses 2 straight x plus 45 degree close parentheses equals square root of 1 minus straight a squared end root  Kemudian  sin invisible function application open parentheses straight x plus 30 degree close parentheses equals straight b equals straight b over 1 end style

begin mathsize 14px style Maka colon space cos space open parentheses straight x plus 30 degree close parentheses equals square root of 1 minus straight b squared end root  Sehingga colon  cos open parentheses 3 straight x plus 75 degree close parentheses space cos open parentheses straight x plus 15 degree close parentheses  equals cos open square brackets open parentheses 2 straight x plus 45 degree close parentheses plus open parentheses straight x plus 30 degree close parentheses close square brackets space cos open square brackets open parentheses 2 straight x plus 45 degree close parentheses minus open parentheses straight x plus 30 degree close parentheses close square brackets  equals open parentheses cos open parentheses 2 straight x plus 45 degree close parentheses space cos open parentheses straight x plus 30 degree close parentheses minus sin open parentheses 2 straight x plus 45 degree close parentheses space sin open parentheses straight x plus 30 degree close parentheses close parentheses open parentheses cos space open parentheses 2 straight x plus 45 degree close parentheses space cos space open parentheses straight x plus 30 degree close parentheses plus sin space open parentheses 2 straight x plus 45 degree close parentheses space sin space open parentheses straight x plus 30 degree close parentheses close parentheses  maka colon  equals open parentheses square root of 1 minus straight a squared end root square root of 1 minus straight b squared end root minus ab close parentheses open parentheses square root of 1 minus straight a squared end root square root of 1 minus straight b squared end root plus ab close parentheses  equals open parentheses open parentheses 1 minus straight a squared close parentheses open parentheses 1 minus straight b squared close parentheses minus straight a squared straight b squared close parentheses  equals 1 minus straight b squared minus straight a squared plus straight a squared straight b squared minus straight a squared straight b squared  equals 1 minus straight b squared minus straight a squared end style

206

4.5 (2 rating)

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Jika diketahui cosα=54​ dan cosβ=1312​, hitunglah bentuk berikut : a. cos(2π​−α),untuk0<α<2π​ b. cos(2π​+α),untuk0<α<2π​

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