Pertanyaan

sin 2 ( 4 π + 4 x ) − sin 2 ( 4 π − 4 x ) = ....

$sin^{2} (\frac{π}{4} + \frac{x}{4}) - sin^{2} (\frac{π}{4} - \frac{x}{4}) = ....$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa . Sehingga : Ingat bahwa : Sehingga : Dan Sehingga : Karena 2 sinA cosA = sin 2A, maka : Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa . Sehingga :

Ingat bahwa :

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

Sehingga :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin invisible function application open parentheses straight pi over 4 plus straight x over 4 close parentheses plus sin invisible function application open parentheses straight pi over 4 minus straight x over 4 close parentheses end cell row blank equals cell 2 space sin invisible function application open parentheses fraction numerator open parentheses straight pi over 4 plus straight x over 4 close parentheses plus open parentheses straight pi over 4 minus straight x over 4 close parentheses over denominator 2 end fraction close parentheses space cos invisible function application open parentheses fraction numerator open parentheses straight pi over 4 plus straight x over 4 close parentheses plus open parentheses straight pi over 4 minus straight x over 4 close parentheses over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space sin invisible function application open parentheses fraction numerator 2 times begin display style straight pi over 4 end style over denominator 2 end fraction close parentheses space cos invisible function application open parentheses fraction numerator 2 times begin display style straight x over 4 end style over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space sin invisible function application straight pi over 4 space cos invisible function application straight x over 4 end cell row blank equals cell 2 times 1 half space square root of 2 times cos invisible function application straight x over 4 end cell row blank equals cell square root of 2 space cos invisible function application straight x over 4 end cell end table end style$

Dan

$begin mathsize 14px style sin invisible function application open parentheses straight pi over 4 plus straight x over 4 close parentheses minus sin invisible function application open parentheses straight pi over 4 minus straight x over 4 close parentheses equals 2 space cos invisible function application open parentheses fraction numerator open parentheses straight pi over 4 plus straight x over 4 close parentheses plus open parentheses straight pi over 4 minus straight x over 4 close parentheses over denominator 2 end fraction close parentheses space space sin invisible function application open parentheses fraction numerator open parentheses straight pi over 4 plus straight x over 4 close parentheses plus open parentheses straight pi over 4 minus straight x over 4 close parentheses over denominator 2 end fraction close parentheses 2 space cos invisible function application open parentheses fraction numerator 2 times begin display style straight pi over 4 end style over denominator 2 end fraction close parentheses space sin invisible function application open parentheses fraction numerator 2 times begin display style straight x over 4 end style over denominator 2 end fraction close parentheses equals 2 space cos invisible function application straight pi over 4 sin invisible function application straight x over 4 equals 2 times 1 half square root of 2 times sin invisible function application straight x over 4 equals square root of 2 space space sin invisible function application straight x over 4 end style$

Sehingga :

Karena 2 sinA cosA = sin 2A, maka :

Jadi, jawaban yang tepat adalah C.