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Nilai dari cos 10 5 ∘ − cos 1 5 ∘ sin 7 5 ∘ + sin 1 5 ∘ ​ = ...

Nilai dari  = ...

  1. begin mathsize 12px style negative 1 third square root of 3 end style

  2. begin mathsize 12px style negative 1 half square root of 3 end style

  3. -1

  4. begin mathsize 12px style 1 half end style

  5. 1

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

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Pembahasan

Ingat! sin A + sin B = 2 sin (A + B) . cos (A - B) sin A -sin B = -2 sin (A + B) . cos (A - B) sin A = cos

Ingat!

  • sin A + sin B = 2 sinbegin mathsize 12px style 1 half end style (A + B) . cosbegin mathsize 12px style 1 half end style (A - B)
  • sin A - sin B = -2 sinbegin mathsize 12px style 1 half end style (A + B) . cosbegin mathsize 12px style 1 half end style (A - B)
  • sin A = cosbegin mathsize 12px style open parentheses 90 degree minus A close parentheses end style

begin mathsize 12px style fraction numerator sin space 75 degree plus sin space 15 degree over denominator cos space 105 degree minus cos space 15 degree end fraction  equals fraction numerator 2 sin begin display style 1 half end style open parentheses 75 degree plus 15 degree close parentheses times cos begin display style 1 half end style open parentheses 75 degree minus 15 degree close parentheses over denominator negative 2 sin 1 half open parentheses 105 degree plus 15 degree close parentheses times sin 1 half open parentheses 105 degree minus 15 degree close parentheses end fraction  equals fraction numerator 2 sin 45 times cos 30 over denominator negative 2 sin 60 times sin 45 end fraction  equals fraction numerator 2 sin 45 times cos 30 over denominator negative 2 cos 30 times sin 45 end fraction  equals negative 1  end style

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Bentuk sederhana dari cos p − cos 5 p sin p + sin 5 p ​ adalah ....

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