sin2(8π​+2A​)−sin2(8π​−2A​)=...

Pertanyaan

sin squared open parentheses straight pi over 8 plus A over 2 close parentheses minus sin squared open parentheses straight pi over 8 minus A over 2 close parentheses equals...

  1. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 space sin space straight pi over 8 end cell end table

  2. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space A space sin space straight pi over 8 end cell end table

  3. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half sin space A end cell end table

  4. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator square root of 2 end fraction sin space A end cell row blank blank blank end table

  5. table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator square root of 2 end fraction cos space A end cell row blank blank blank end table

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Ingat rumus jumlah dan selisih trigonometri berikut ini:

sin space A plus sin space B equals 2 space sin space 1 half open parentheses A plus B close parentheses space cos space 1 half open parentheses A minus B close parentheses

sin space A minus sin space B equals 2 space cos space 1 half open parentheses A plus B close parentheses space sin space 1 half open parentheses A minus B close parentheses

Dengan menggunakan konsep di atas, diperoleh hasil:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space open parentheses straight pi over 8 plus A over 2 close parentheses plus sin space open parentheses straight pi over 8 minus A over 2 close parentheses end cell row blank equals cell 2 space sin space 1 half open square brackets open parentheses straight pi over 8 plus A over 2 close parentheses plus open parentheses straight pi over 8 minus A over 2 close parentheses close square brackets space cos space 1 half open square brackets open parentheses straight pi over 8 plus A over 2 close parentheses minus open parentheses straight pi over 8 minus A over 2 close parentheses close square brackets end cell row blank equals cell 2 space sin space 1 half open parentheses fraction numerator 2 straight pi over denominator 8 end fraction close parentheses space cos space 1 half open parentheses fraction numerator 2 straight A over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space sin space open parentheses straight pi over 8 close parentheses space cos space open parentheses straight A over 2 close parentheses end cell row blank blank blank row blank blank blank row blank blank cell sin space open parentheses straight pi over 8 plus A over 2 close parentheses minus sin space open parentheses straight pi over 8 minus A over 2 close parentheses end cell row blank equals cell 2 space cos space 1 half open square brackets open parentheses straight pi over 8 plus A over 2 close parentheses plus open parentheses straight pi over 8 minus A over 2 close parentheses close square brackets space sin space 1 half open square brackets open parentheses straight pi over 8 plus A over 2 close parentheses minus open parentheses straight pi over 8 minus A over 2 close parentheses close square brackets end cell row blank equals cell 2 space cos space 1 half open parentheses fraction numerator 2 straight pi over denominator 8 end fraction close parentheses space sin space 1 half open parentheses fraction numerator 2 straight A over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space cos space open parentheses straight pi over 8 close parentheses space sin space open parentheses straight A over 2 close parentheses end cell end table

Maka

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin squared open parentheses straight pi over 8 plus A over 2 close parentheses minus sin squared open parentheses straight pi over 8 minus A over 2 close parentheses end cell row blank equals cell open square brackets sin space open parentheses straight pi over 8 plus A over 2 close parentheses plus sin space open parentheses straight pi over 8 minus A over 2 close parentheses close square brackets cross times open square brackets sin space open parentheses straight pi over 8 plus A over 2 close parentheses minus sin space open parentheses straight pi over 8 minus A over 2 close parentheses close square brackets end cell row blank equals cell 2 space sin space open parentheses straight pi over 8 close parentheses space cos space open parentheses A over 2 close parentheses cross times 2 space cos space open parentheses straight pi over 8 close parentheses space sin space open parentheses A over 2 close parentheses end cell row blank equals cell 2 space sin space open parentheses straight pi over 8 close parentheses space cos space open parentheses straight pi over 8 close parentheses cross times 2 space sin space open parentheses A over 2 close parentheses space cos space open parentheses A over 2 close parentheses end cell row blank equals cell space sin space open parentheses fraction numerator 2 straight pi over denominator 8 end fraction close parentheses space sin space A end cell row blank equals cell fraction numerator 1 over denominator square root of 2 end fraction sin space A end cell row blank blank blank end table

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared open parentheses straight pi over 8 plus A over 2 close parentheses minus sin squared open parentheses straight pi over 8 minus A over 2 close parentheses end cell equals cell fraction numerator 1 over denominator square root of 2 end fraction sin space A end cell row blank blank blank end table.

Oleh karena itu, jawaban yang tepat adalah D.

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