Pertanyaan

Nilai dari sin 2 0 ∘ − cos 2 0 ∘ sin 2 0 ∘ + cos 2 0 ∘ adalah ....

Nilai dari $\frac{sin 2 0 ^{\circ} + cos 2 0 ^{\circ}}{sin 2 0 ^{\circ} - cos 2 0 ^{\circ}}$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa : Sehingga : Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa :

Sehingga :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin invisible function application 20 degree plus cos invisible function application 20 degree over denominator sin invisible function application 20 degree minus cos invisible function application 20 degree end fraction end cell equals cell fraction numerator cos invisible function application 70 degree plus cos invisible function application 20 degree over denominator cos invisible function application 70 degree minus cos invisible function application 20 degree end fraction end cell row blank equals cell fraction numerator 2 cos open parentheses begin display style fraction numerator 70 degree plus 20 degree over denominator 2 end fraction end style close parentheses cos open parentheses begin display style fraction numerator 70 degree minus 20 degree over denominator 2 end fraction end style close parentheses over denominator negative 2 sin open parentheses begin display style fraction numerator 70 degree plus 20 degree over denominator 2 end fraction end style close parentheses sin open parentheses begin display style fraction numerator 70 degree minus 20 degree over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell negative fraction numerator cos open parentheses begin display style fraction numerator 90 degree over denominator 2 end fraction end style close parentheses cos open parentheses begin display style fraction numerator 50 degree over denominator 2 end fraction end style close parentheses over denominator sin open parentheses begin display style fraction numerator 90 degree over denominator 2 end fraction end style close parentheses sin open parentheses begin display style fraction numerator 50 degree over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell negative fraction numerator cos 45 degree cos 25 degree over denominator sin 45 degree sin 25 degree end fraction end cell row blank equals cell negative fraction numerator begin display style 1 half end style square root of 2. cos space 25 degree over denominator begin display style 1 half end style square root of 2. sin 25 degree end fraction end cell row blank equals cell negative fraction numerator cos invisible function application 25 degree over denominator sin invisible function application 25 degree end fraction end cell row blank equals cell negative cot invisible function application 25 degree end cell row blank equals cell negative cot invisible function application left parenthesis 90 degree minus 65 degree right parenthesis space end cell row blank equals cell negative tan invisible function application 65 degree end cell end table end style$

Jadi, jawaban yang tepat adalah A.