Pertanyaan

sin 2 ( 6 π − x ) − sin 2 ( 6 π + x ) = ....

$sin^{2} (\frac{π}{6} - x) - sin^{2} (\frac{π}{6} + x) = ....$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan bahwa . Sehingga : Ingat bahwa : Sehingga : Ingat bahwa cos (–x) = cos x. Sehingga : Dan Ingat bahwa sin (–x) = –sin x. Sehingga : Sehingga : Karena 2 sinA cos A = sin 2A, maka : Jadi, jawaban yang tepat adalah D.

Perhatikan bahwa . Sehingga :

Ingat bahwa :

$begin mathsize 14px style sin invisible function application straight alpha plus sin invisible function application straight beta equals 2 space sin invisible function application open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space cos invisible function application open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses sin invisible function application straight alpha minus sin invisible function application straight beta equals 2 space cos invisible function application open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses space space sin invisible function application open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses end style$

Sehingga :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin invisible function application open parentheses straight pi over 6 minus straight x close parentheses plus sin invisible function application open parentheses straight pi over 6 plus straight x close parentheses end cell row blank equals cell 2 space sin invisible function application open parentheses fraction numerator open parentheses straight pi over 6 minus straight x close parentheses plus open parentheses straight pi over 6 plus straight x close parentheses over denominator 2 end fraction close parentheses space cos invisible function application open parentheses fraction numerator open parentheses straight pi over 6 minus straight x close parentheses plus open parentheses straight pi over 6 plus straight x close parentheses over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space sin invisible function application open parentheses fraction numerator 2 times straight pi over 6 over denominator 2 end fraction close parentheses space cos invisible function application open parentheses fraction numerator 2 times left parenthesis negative straight x right parenthesis over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space sin invisible function application straight pi over 6 space cos invisible function application left parenthesis negative straight x right parenthesis end cell end table end style$

Ingat bahwa cos (–x) = cos x. Sehingga :

Dan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin invisible function application open parentheses straight pi over 6 minus straight x close parentheses minus sin invisible function application open parentheses straight pi over 6 plus straight x close parentheses end cell row blank equals cell 2 space cos invisible function application open parentheses fraction numerator open parentheses straight pi over 6 minus straight x close parentheses plus open parentheses straight pi over 6 plus straight x close parentheses over denominator 2 end fraction close parentheses space space sin invisible function application open parentheses fraction numerator open parentheses straight pi over 6 minus straight x close parentheses minus open parentheses straight pi over 6 plus straight x close parentheses over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space cos invisible function application open parentheses fraction numerator 2 times straight pi over 6 over denominator 2 end fraction close parentheses space sin invisible function application open parentheses fraction numerator 2 times left parenthesis negative straight x right parenthesis over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space cos invisible function application straight pi over 6 space space sin invisible function application left parenthesis negative straight x right parenthesis end cell end table end style$

Ingat bahwa sin (–x) = – sin x. Sehingga :

Sehingga :

Karena 2 sinA cos A = sin 2A, maka :

Jadi, jawaban yang tepat adalah D.