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Pertanyaan

Jika sin(2x + 60°) = a dan sin(x + 45°) = b, maka cos(3x + 105°) 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

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Pembahasan

begin mathsize 14px style box enclose Ingat factorial  space space cos space invisible function application straight alpha equals square root of 1 minus sin squared space invisible function application straight alpha end root space space end enclose    Maka  cos invisible function application open parentheses 2 straight x plus 60 to the power of straight o close parentheses equals square root of 1 minus sin squared space invisible function application open parentheses 2 straight x plus 60 to the power of straight o close parentheses end root equals square root of 1 minus straight a squared end root  cos invisible function application open parentheses straight x plus 45 to the power of straight o close parentheses equals square root of 1 minus sin squared space invisible function application open parentheses straight x plus 45 to the power of straight o close parentheses end root equals square root of 1 minus straight b squared end root    box enclose Ingat  space space cos invisible function application open parentheses straight alpha plus straight beta close parentheses equals cos invisible function application space straight alpha space cos invisible function application space straight beta minus sin space invisible function application straight alpha space sin invisible function application space straight beta space space  space space cos invisible function application open parentheses straight alpha minus straight beta close parentheses equals cos invisible function application space straight alpha space cos invisible function application space straight beta plus sin invisible function application space straight alpha space sin invisible function application space straight beta end enclose    Maka  cos invisible function application open parentheses 3 straight x plus 105 to the power of straight o close parentheses equals cos invisible function application open parentheses open parentheses 2 straight x plus 60 to the power of straight o close parentheses plus open parentheses straight x plus 45 to the power of straight o close parentheses close parentheses  equals cos invisible function application open parentheses 2 straight x plus 60 to the power of straight o close parentheses space cos invisible function application open parentheses straight x plus 45 to the power of straight o close parentheses minus sin invisible function application open parentheses 2 straight x plus 60 to the power of straight o close parentheses space sin invisible function application open parentheses straight x plus 45 to the power of straight o close parentheses  equals square root of 1 minus straight a squared end root. square root of 1 minus straight b squared end root minus straight a. straight b  dan  cos invisible function application open parentheses straight x plus 15 to the power of straight o close parentheses equals cos invisible function application open parentheses open parentheses 2 straight x plus 60 to the power of straight o close parentheses minus open parentheses straight x plus 45 to the power of straight o close parentheses close parentheses  equals cos invisible function application open parentheses 2 straight x plus 60 to the power of straight o close parentheses space cos invisible function application open parentheses straight x plus 45 to the power of straight o close parentheses plus sin invisible function application open parentheses 2 straight x plus 60 to the power of straight o close parentheses space sin invisible function application open parentheses straight x plus 45 to the power of straight o close parentheses  equals square root of 1 minus straight a squared end root. square root of 1 minus straight b squared end root plus straight a. straight b    Sehingga  sin invisible function application open parentheses 3 straight x plus 105 to the power of straight o close parentheses space sin invisible function application open parentheses straight x plus 15 to the power of straight o close parentheses equals open parentheses square root of 1 minus straight a squared end root. square root of 1 minus straight b squared end root minus straight a. straight b 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 straight a. straight b close parentheses  equals open parentheses square root of 1 minus straight a squared end root. square root of 1 minus straight b squared end root close parentheses squared minus open parentheses straight a. straight b close parentheses squared equals 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  equals open parentheses 1 minus straight a squared minus straight b squared plus straight a squared straight b squared close parentheses minus straight a squared straight b squared equals 1 minus straight a squared minus straight b squared end style

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