Pertanyaan

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

Nilai dari $\frac{sin 10 5 ^{\circ} + sin 1 5 ^{\circ}}{sin 7 5 ^{\circ} - cos 1 5 ^{\circ}} =$ ...

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Pembahasan

Perbandingan trigonometri sudut-sudut berelasi yaitu: Sehingga diperoleh: Nilai sudut trigonometrinya yaitu: Maka, nilai dari .

Perbandingan trigonometri sudut-sudut berelasi yaitu:

table row cell sin space open parentheses 90 degree minus alpha close parentheses end cell equals cell cos space alpha end cell row cell sin space open parentheses 90 degree plus alpha close parentheses end cell equals cell cos space alpha end cell end table

Sehingga diperoleh:

Nilai sudut trigonometrinya yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 105 degree plus sin space 15 degree over denominator sin space 75 degree minus cos space 15 degree end fraction end cell equals cell fraction numerator open parentheses begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 close parentheses plus open parentheses begin display style 1 fourth end style square root of 6 minus begin display style 1 fourth end style square root of 2 close parentheses over denominator open parentheses begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 close parentheses minus open parentheses begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 minus begin display style 1 fourth end style square root of 2 over denominator begin display style 1 fourth end style square root of 6 minus begin display style 1 fourth end style square root of 6 plus begin display style 1 fourth end style square root of 2 minus begin display style 1 fourth end style square root of 2 end fraction end cell row blank equals cell fraction numerator begin display style 2 over 4 end style square root of 6 over denominator 0 end fraction end cell row blank equals infinity end table$

Maka, nilai dari $fraction numerator sin space 105 degree plus sin space 15 degree over denominator sin space 75 degree minus cos space 15 degree end fraction equals infinity$ .

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