Pertanyaan

sin 2 ( 10 5 ∘ ) − sin 2 ( 1 5 ∘ ) = ....

$sin^{2} (10 5^{\circ}) - sin^{2} (1 5^{\circ}) = ....$

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Habis dalam

Klaim

R. Mahmudah

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa . Sehingga : Ingat bahwa : Sehingga : Dan Sehingga Jadi, jawaban yang tepat adalah C.

Perhatikan bahwa . Sehingga :

Ingat bahwa :

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

Sehingga :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin invisible function application 105 degree plus sin invisible function application 15 degree end cell row blank equals cell 2 space sin invisible function application open parentheses fraction numerator 105 degree plus 15 degree over denominator 2 end fraction close parentheses space space cos invisible function application open parentheses fraction numerator 105 degree minus 15 degree over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space sin invisible function application open parentheses fraction numerator 120 degree over denominator 2 end fraction close parentheses space space cos invisible function application open parentheses fraction numerator 90 degree over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space sin invisible function application 60 degree space space cos invisible function application 45 degree end cell row blank equals cell 2.1 half square root of 3.1 half square root of 2 end cell row blank equals cell 1 half square root of 6 end cell end table end style$

Dan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin invisible function application 105 degree minus sin invisible function application 15 degree end cell row blank equals cell 2 space cos invisible function application open parentheses fraction numerator 105 degree plus 15 degree over denominator 2 end fraction close parentheses space space sin invisible function application open parentheses fraction numerator 105 degree minus 15 degree over denominator 2 end fraction close parentheses end cell row blank equals cell 2 cos invisible function application open parentheses fraction numerator 120 degree over denominator 2 end fraction close parentheses space space sin invisible function application open parentheses fraction numerator 90 degree over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space cos invisible function application 60 degree space space sin invisible function application 45 degree end cell row blank equals cell 2.1 half.1 half square root of 2 end cell row blank equals cell 1 half square root of 2 end cell end table end style$

Sehingga

Jadi, jawaban yang tepat adalah C.