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Nilai dari cos 10 5 ∘ − cos 1 5 ∘ sin 10 5 ∘ − sin 1 5 ∘ = ...

Nilai dari $\frac{sin 10 5 ^{\circ} - sin 1 5 ^{\circ}}{cos 10 5 ^{\circ} - cos 1 5 ^{\circ}}$ = ...

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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$begin mathsize 12px style sin alpha minus sin beta equals 2 cos fraction numerator open parentheses alpha plus beta close parentheses over denominator 2 end fraction times sin fraction numerator open parentheses alpha minus beta close parentheses over denominator 2 end fraction cos alpha minus cos beta equals negative 2 sin fraction numerator open parentheses alpha plus beta close parentheses over denominator 2 end fraction times sin fraction numerator open parentheses alpha minus beta close parentheses over denominator 2 end fraction fraction numerator sin 105 degree minus sin 15 degree over denominator cos 105 degree minus cos 15 degree end fraction equals fraction numerator 2 cos begin display style fraction numerator open parentheses 105 degree plus 15 degree close parentheses over denominator 2 end fraction end style times sin begin display style fraction numerator open parentheses 105 degree minus 15 degree close parentheses over denominator 2 end fraction end style over denominator negative 2 sin begin display style fraction numerator open parentheses 105 degree minus 15 degree close parentheses over denominator 2 end fraction end style times sin begin display style fraction numerator open parentheses 105 degree minus 15 degree close parentheses over denominator 2 end fraction end style end fraction equals fraction numerator 2 times begin display style 1 half end style times begin display style 1 half end style times square root of 2 over denominator negative 2 times begin display style 1 half end style square root of 3 times begin display style 1 half end style square root of 2 end fraction equals fraction numerator begin display style 1 half end style square root of 2 over denominator negative begin display style 1 half end style square root of 6 end fraction equals 1 third square root of 3 end style$

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