Pertanyaan

cos⁡ α ⋅ cos⁡ 2α ⋅ cos ⁡4α ⋅ cos ⁡8α⋅…⋅cos⁡ 2 2020 α = ....

cos⁡ α ⋅ cos⁡ 2α ⋅ cos ⁡4α ⋅ cos ⁡8α⋅…⋅cos⁡ 2²⁰²⁰ α = ....

$begin mathsize 14px style fraction numerator sin invisible function application 2 to the power of 2021 straight alpha over denominator 2 to the power of 2021 sin invisible function application straight alpha end fraction end style$
$begin mathsize 14px style fraction numerator sin invisible function application 2 to the power of 2020 straight alpha over denominator 2 to the power of 2020 sin invisible function application straight alpha end fraction end style$
$begin mathsize 14px style fraction numerator 2 to the power of 2020 sin invisible function application straight alpha over denominator sin invisible function application 2 to the power of 2020 straight alpha end fraction end style$
$begin mathsize 14px style fraction numerator 2 to the power of 2021 sin invisible function application straight alpha over denominator sin invisible function application 2 to the power of 2021 straight alpha end fraction end style$

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A. Abdul

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

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

Perhatikan bahwa

$begin mathsize 14px style cos invisible function application straight alpha times cos invisible function application 2 straight alpha times cos invisible function application 4 straight alpha times cos invisible function application 8 straight alpha times horizontal ellipsis times cos invisible function application 2 to the power of 2020 straight alpha equals fraction numerator sin invisible function application straight alpha over denominator sin invisible function application straight alpha end fraction times cos invisible function application straight alpha times cos invisible function application 2 straight alpha times cos invisible function application 4 straight alpha times cos invisible function application 8 straight alpha times horizontal ellipsis times cos invisible function application 2 to the power of 2020 straight alpha equals fraction numerator sin invisible function application straight alpha times cos invisible function application straight alpha times cos invisible function application 2 straight alpha times cos invisible function application 4 straight alpha times cos invisible function application 8 straight alpha times horizontal ellipsis times cos invisible function application 2 to the power of 2020 straight alpha over denominator sin invisible function application straight alpha end fraction end style$

Ingat bahwa

Sehingga

$begin mathsize 14px style table attributes columnalign left end attributes row cell fraction numerator sinα times cosα times cos 2 straight alpha times cos 4 straight alpha times cos 8 straight alpha times horizontal ellipsis times cos 2 to the power of 2020 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator 1 half sin 2 straight alpha times cos 2 straight alpha times cos 4 straight alpha times cos 8 straight alpha times horizontal ellipsis times cos 2 to the power of 2020 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator 1 half times 1 half sin 4 straight alpha times cos 4 straight alpha times cos 8 straight alpha times horizontal ellipsis times cos 2 to the power of 2020 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator 1 fourth sin 4 straight alpha times cos 4 straight alpha times cos 8 straight alpha times horizontal ellipsis times cos 2 to the power of 2020 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator 1 fourth times 1 half sin 8 straight alpha times cos 8 straight alpha times horizontal ellipsis times cos 2 to the power of 2020 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator 1 over 8 sin 8 straight alpha times cos 8 straight alpha times horizontal ellipsis times cos 2 to the power of 2020 straight alpha over denominator sinα end fraction end cell row cell equals horizontal ellipsis end cell row cell equals fraction numerator 1 over 2 to the power of 2020 sin 2 to the power of 2020 straight alpha times cos 2 to the power of 2020 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator 1 over 2 to the power of 2020 times 1 half sin 2 to the power of 2021 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator 1 over 2 to the power of 2021 sin 2 to the power of 2021 straight alpha over denominator sinα end fraction end cell row cell equals fraction numerator sin 2 to the power of 2021 straight alpha over denominator 2 to the power of 2021 sinα end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah A.