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Pertanyaan

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

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

  1. begin mathsize 14px style open parentheses a minus b close parentheses squared end style

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

  3. begin mathsize 14px style fraction numerator a squared over denominator square root of 2 end fraction minus fraction numerator begin display style b squared end style over denominator begin display style square root of 2 end style end fraction end style

  4. begin mathsize 14px style a squared minus fraction numerator 2 a b over denominator square root of 6 end fraction plus b squared end style

  5. begin mathsize 14px style 2 a b minus fraction numerator 1 over denominator square root of 6 end fraction end style

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

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Pembahasan

begin mathsize 14px style text i) Tentukan nilai cos dari tiap bentuk end text  text Ingat! end text  c o s space alpha equals square root of 1 minus s i n squared space alpha end root  text Maka end text  c o s open parentheses 2 x plus 30 to the power of o close parentheses equals square root of 1 minus s i n squared open parentheses 2 x plus 30 to the power of o close parentheses end root equals square root of 1 minus a squared end root  c o s open parentheses x plus 45 to the power of o close parentheses equals square root of 1 minus s i n squared open parentheses x plus 45 to the power of o close parentheses end root equals square root of 1 minus b squared end root    text ii) end text text Perhatikan rumus untuk fungsi sin end text  text Ingat! end text  s i n open parentheses alpha plus beta close parentheses equals s i n space alpha space c o s space beta plus c o s space alpha space s i n space beta  s i n open parentheses alpha minus beta close parentheses equals s i n space alpha space c o s space beta minus c o s space alpha space s i n space beta  text Maka end text  sin open parentheses 3 x plus 75 to the power of o close parentheses equals sin open parentheses open parentheses 2 x plus 30 to the power of o close parentheses plus open parentheses x plus 45 to the power of o close parentheses close parentheses  equals sin open parentheses 2 x plus 30 to the power of o close parentheses cos open parentheses x plus 45 to the power of o close parentheses plus cos open parentheses 2 x plus 30 to the power of o close parentheses sin open parentheses x plus 45 to the power of o close parentheses  equals a bullet square root of 1 minus b squared end root plus square root of 1 minus a squared end root bullet b  text dan end text  sin open parentheses x minus 15 to the power of o close parentheses equals sin open parentheses open parentheses 2 x plus 30 to the power of o close parentheses minus open parentheses x plus 45 to the power of o close parentheses close parentheses  equals sin open parentheses 2 x plus 30 to the power of o close parentheses cos open parentheses x plus 45 to the power of o close parentheses minus cos open parentheses 2 x plus 30 to the power of o close parentheses sin open parentheses x plus 45 to the power of o close parentheses  equals a bullet square root of 1 minus b squared end root minus square root of 1 minus a squared end root bullet b  text sehingga end text  sin open parentheses 3 x plus 75 to the power of o close parentheses sin open parentheses x minus 15 to the power of o close parentheses equals open parentheses a bullet square root of 1 minus b squared end root plus square root of 1 minus a squared end root bullet b close parentheses open parentheses a bullet square root of 1 minus b squared end root minus square root of 1 minus a squared end root bullet b close parentheses  equals open parentheses a bullet square root of 1 minus b squared end root close parentheses squared minus open parentheses square root of 1 minus a squared end root bullet b close parentheses squared equals a squared open parentheses 1 minus b squared close parentheses minus open parentheses 1 minus a squared close parentheses b squared equals a squared minus a squared b squared minus b squared plus a squared b squared  equals a squared minus b squared end style

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Buktikan: b. sin ( x + y ) ⋅ sin ( x − y ) = sin 2 x − sin 2 y .

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