Pertanyaan

Nilai dari cos 4 5 ∘ + cos 6 0 ∘ sin 4 5 ∘ + sin 6 0 ∘ − cos 3 0 ∘ + cos 4 5 ∘ sin 3 0 ∘ + sin 4 5 ∘ adalah ....

Nilai dari $\frac{sin 4 5 ^{\circ} + sin 6 0 ^{\circ}}{cos 4 5 ^{\circ} + cos 6 0 ^{\circ}} - \frac{sin 3 0 ^{\circ} + sin 4 5 ^{\circ}}{cos 3 0 ^{\circ} + cos 4 5 ^{\circ}}$ adalah ....

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Klaim

R. Rohmat

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan tabel berikut! Oleh karena itu, didapat Jadi, jawaban yang tepat adalah C.

Perhatikan tabel berikut!

Oleh karena itu, didapat

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin invisible function application 45 degree plus sin invisible function application 60 degree over denominator cos invisible function application 45 degree plus cos invisible function application 60 degree end fraction minus fraction numerator sin invisible function application 30 degree plus sin invisible function application 45 degree over denominator cos invisible function application 30 degree plus cos invisible function application 45 degree end fraction end cell row blank equals cell fraction numerator 1 half square root of 2 plus 1 half square root of 3 over denominator 1 half square root of 2 plus 1 half end fraction minus fraction numerator 1 half plus 1 half square root of 2 over denominator 1 half square root of 3 plus 1 half square root of 2 end fraction end cell row blank equals cell fraction numerator 1 half open parentheses square root of 2 plus square root of 3 close parentheses over denominator 1 half open parentheses square root of 2 plus 1 close parentheses end fraction minus fraction numerator 1 half open parentheses 1 plus square root of 2 close parentheses over denominator 1 half open parentheses square root of 3 plus square root of 2 close parentheses end fraction end cell row blank equals cell fraction numerator square root of 2 plus square root of 3 over denominator square root of 2 plus 1 end fraction minus fraction numerator 1 plus square root of 2 over denominator square root of 3 plus square root of 2 end fraction end cell row blank equals cell fraction numerator square root of 2 plus square root of 3 over denominator square root of 2 plus 1 end fraction times fraction numerator square root of 2 minus 1 over denominator square root of 2 minus 1 end fraction minus fraction numerator 1 plus square root of 2 over denominator square root of 3 plus square root of 2 end fraction times fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 minus square root of 2 end fraction end cell row blank equals cell fraction numerator open parentheses square root of 2 plus square root of 3 close parentheses open parentheses square root of 2 minus 1 close parentheses over denominator 2 minus 1 end fraction minus fraction numerator open parentheses 1 plus square root of 2 close parentheses open parentheses square root of 3 minus square root of 2 close parentheses over denominator 3 minus 2 end fraction end cell row blank equals cell fraction numerator 2 minus square root of 2 plus square root of 6 minus square root of 3 over denominator 1 end fraction minus fraction numerator square root of 3 minus square root of 2 plus square root of 6 minus 2 over denominator 1 end fraction end cell row blank equals cell open parentheses 2 minus square root of 2 plus square root of 6 minus square root of 3 close parentheses minus open parentheses square root of 3 minus square root of 2 plus square root of 6 minus 2 close parentheses end cell row blank equals cell 2 minus square root of 2 plus square root of 6 minus square root of 3 minus square root of 3 plus square root of 2 minus square root of 6 plus 2 end cell row blank equals cell 4 minus 2 square root of 3 end cell end table end style$

Jadi, jawaban yang tepat adalah C.