Pertanyaan

cos ( 3 π − x ) sin x − sin ( 3 π + x ) cos ( 3 2 π − x ) = ....

$cos (\frac{π}{3} - x) sin x - sin (\frac{π}{3} + x) cos (\frac{2 π}{3} - x) =$ ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat bahwa Sehingga Selanjutnya Ingat bahwa Maka Sehingga Jadi, jawaban yang tepat adalah A.

Ingat bahwa

Sehingga

Selanjutnya

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin invisible function application open parentheses pi over 3 plus x close parentheses cos invisible function application open parentheses fraction numerator 2 pi over denominator 3 end fraction minus x close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application open parentheses open parentheses pi over 3 plus x close parentheses plus open parentheses fraction numerator 2 pi over denominator 3 end fraction minus x close parentheses close parentheses plus sin invisible function application open parentheses open parentheses pi over 3 plus x close parentheses minus open parentheses fraction numerator 2 pi over denominator 3 end fraction minus x close parentheses close parentheses close parentheses end cell row blank equals cell 1 half open parentheses sin invisible function application pi plus sin invisible function application open parentheses negative pi over 3 plus 2 x close parentheses close parentheses end cell row blank equals cell 1 half open parentheses 0 plus sin invisible function application open parentheses negative pi over 3 plus 2 x close parentheses close parentheses end cell row blank equals cell 1 half sin invisible function application open parentheses negative pi over 3 plus 2 x close parentheses end cell row blank equals cell 1 half sin invisible function application open parentheses negative open parentheses pi over 3 minus 2 x close parentheses close parentheses end cell row blank blank blank end table end style$

Ingat bahwa

Maka

Sehingga

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell cos invisible function application open parentheses pi over 3 minus x close parentheses sin invisible function application x minus sin invisible function application open parentheses pi over 3 plus x close parentheses cos invisible function application open parentheses fraction numerator 2 pi over denominator 3 end fraction minus x close parentheses end cell row blank equals cell open parentheses 1 fourth square root of 3 minus 1 half sin invisible function application open parentheses pi over 3 minus 2 x close parentheses close parentheses minus open parentheses negative 1 half sin invisible function application open parentheses pi over 3 minus 2 x close parentheses close parentheses end cell row blank equals cell 1 fourth square root of 3 minus 1 half sin invisible function application open parentheses pi over 3 minus 2 x close parentheses plus 1 half sin invisible function application open parentheses pi over 3 minus 2 x close parentheses end cell row blank equals cell 1 fourth square root of 3 end cell row blank blank blank row blank blank blank end table end style$

Jadi, jawaban yang tepat adalah A.