Pertanyaan

Jika A , B , C adalah sudut-sudut sebuah segitiga, buktikan setiap pernyataan berikut. c. tan C = tan A ⋅ tan B − 1 tan A + tan B

Jika $A, B, C$ adalah sudut-sudut sebuah segitiga, buktikan setiap pernyataan berikut.

c. $tan C = \frac{tan A + tan B}{tan A \cdot tan B - 1}$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $tan space straight C equals fraction numerator tan space straight A plus tan space straight B over denominator tan space straight A times tan space straight B minus 1 end fraction$ .

Pembahasan

Ingat kembali: Diketahui adalah sudut-sudut sebuah segitiga. Akan dibuktikan . Maka: - Ubah bentuk ruas kiri - Ubah bentuk ruas kanan Sehingga: Jadi, terbukti bahwa .

Ingat kembali:

$tan space straight A equals fraction numerator sin space straight A over denominator cos space straight A end fraction tan space open parentheses straight A plus straight B close parentheses equals fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A times tan space straight B end fraction tan space open parentheses 180 degree minus straight A close parentheses equals negative tan space straight A$

Diketahui straight A comma space straight B comma space straight C adalah sudut-sudut sebuah segitiga. Akan dibuktikan $tan space straight C equals fraction numerator tan space straight A plus tan space straight B over denominator tan space straight A times tan space straight B minus 1 end fraction$ . Maka:

- Ubah bentuk ruas kiri

$table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell tan space straight C end cell row blank equals cell tan open parentheses 180 degree minus open parentheses straight A plus straight B close parentheses close parentheses end cell row blank equals cell negative tan open parentheses straight A plus straight B close parentheses end cell row blank equals cell negative open parentheses fraction numerator sin space open parentheses straight A plus straight B close parentheses over denominator cos space open parentheses straight A plus straight B close parentheses end fraction close parentheses end cell row blank equals cell negative open parentheses fraction numerator sin space straight A times cos space straight B plus cos space straight A times sin space straight B over denominator cos space straight A times cos space straight B minus sin space straight A times sin space straight B end fraction close parentheses end cell row blank equals cell fraction numerator sin space straight A times cos space straight B plus cos space straight A times sin space straight B over denominator negative cos space straight A times cos space straight B plus sin space straight A times sin space straight B end fraction end cell row blank equals cell fraction numerator sin space straight A times cos space straight B plus cos space straight A times sin space straight B over denominator sin space straight A times sin space straight B minus cos space straight A times cos space straight B end fraction end cell end table$

- Ubah bentuk ruas kanan

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kanan end cell equals cell fraction numerator tan space straight A plus tan space straight B over denominator tan space straight A times tan space straight B minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator sin space straight A over denominator cos space straight A end fraction end style plus begin display style fraction numerator sin space straight B over denominator cos space straight B end fraction end style over denominator begin display style fraction numerator sin space straight A over denominator cos space straight A end fraction end style times begin display style fraction numerator sin space straight B over denominator cos space straight B end fraction end style minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator sin space straight A times cos space straight B plus cos space straight A times sin space straight B over denominator cos space straight A times cos space straight B end fraction end style over denominator begin display style fraction numerator sin space straight A times sin space straight B minus cos space straight A times cos space straight B over denominator cos space straight A times cos space straight B end fraction end style end fraction end cell row blank equals cell fraction numerator sin space straight A times cos space straight B plus cos space straight A times sin space straight B over denominator up diagonal strike cos space straight A times cos space straight B end strike end fraction cross times fraction numerator up diagonal strike cos space straight A times cos space straight B end strike over denominator sin space straight A times sin space straight B minus cos space straight A times cos space straight B end fraction end cell row blank equals cell fraction numerator sin space straight A times cos space straight B plus cos space straight A times sin space straight B over denominator sin space straight A times sin space straight B minus cos space straight A times cos space straight B end fraction end cell end table end style$

Sehingga:

Ruas space kiri equals Ruas space kanan

Jadi, terbukti bahwa $tan space straight C equals fraction numerator tan space straight A plus tan space straight B over denominator tan space straight A times tan space straight B minus 1 end fraction$ .

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

0.0 (0 rating)

Pertanyaan serupa

6. Dalam sebuah △ A BC , diketahui tan α = − 4 dan cos 2 β = − 169 119 . Tanpa menggunakan daftar atau tabel matematika maupun kalkulator, tentukan tan y , dengan α , β , γ adalah sudut dalam △ A BC...

4.6

Jawaban terverifikasi

Nilai tan 16 5 ∘ = ...

4.7

Jawaban terverifikasi

Buktikan bahwa pernyataan berikut benar. Dalam segitiga ABC berlaku: tan ( A + B ) + tan C = 0

0.0

Jawaban terverifikasi

Nilai dari tan 84 0 ∘ + tan 66 0 ∘ = ...

5.0

Jawaban terverifikasi

Jika tan 4 ∘ = k ,maka nilai dari tan 13 9 ∘ adalah....