Jika A, B, C adalah sudut-sudut sebuah segitiga, buktikan setiap pernyataan berikut. b. sin (2A+B​)=sin 2C​

Pertanyaan

Jika straight A comma space straight B comma space straight C adalah sudut-sudut sebuah segitiga, buktikan setiap pernyataan berikut.

b. sin space open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses equals sin space straight C over 2 

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

terbukti bahwa sin space open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses equals sin space straight C over 2.

Pembahasan

Ingat kembali:

Jumlah space sudut space dalam space segitiga equals 180 degree cos space open parentheses 180 degree minus straight A close parentheses equals negative cos space straight A sin space 1 half straight A equals plus-or-minus square root of fraction numerator 1 minus cos space straight A over denominator 2 end fraction end root cos space 1 half straight A equals plus-or-minus square root of fraction numerator 1 plus cos space straight A over denominator 2 end fraction end root 

Diketahui straight A comma space straight B comma space straight C adalah sudut-sudut sebuah segitiga, maka: 

table attributes columnalign right center left columnspacing 0px end attributes row cell angle straight A plus angle straight B plus angle straight C end cell equals cell 180 degree end cell row cell angle straight A plus angle straight B end cell equals cell 180 degree minus angle straight C end cell end table 

Akan dibuktikan sin space open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses equals sin space straight C over 2, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell sin space open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus cos space open parentheses straight A plus straight B close parentheses over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 minus cos space open parentheses 180 degree minus straight C close parentheses over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus square root of fraction numerator 1 plus cos space straight C over denominator 2 end fraction end root end cell row blank equals cell plus-or-minus cos space straight C over 2 end cell end table  

Jadi, terbukti bahwa sin space open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses equals sin space straight C over 2.

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