Pertanyaan

Tunjukkan apakah berlaku rumus-rumus: a. tan ( A + B ) jika A = B = 3 1 π

Tunjukkan apakah berlaku rumus-rumus:

a. $tan (A + B)$ jika $A = B = \frac{1}{3} π$ $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

jika berlaku rumus sehingga menghasilkanrumus baru yaitu atau .

jika

straight A equals straight B equals 1 third straight pi

berlaku rumus tan space open parentheses straight A plus straight B close parentheses

sehingga menghasilkan rumus baru yaitu tan space 2 straight A

atau

Pembahasan

Rumus Penjumlahan Dua Sudut pada Tangen Sudut Rangkap pada Tangen Adit berlaku rumus jika . atau Jadi, jika berlaku rumus sehingga menghasilkanrumus baru yaitu atau .

Rumus Penjumlahan Dua Sudut pada Tangen

$tan space open parentheses alpha plus beta close parentheses equals fraction numerator tan space alpha plus tan space beta over denominator 1 minus tan space alpha times tan space beta end fraction$

Sudut Rangkap pada Tangen

$tan space 2 alpha equals fraction numerator 2 space tan space alpha over denominator 1 minus tan squared space alpha end fraction$

Adit berlaku rumus tan space open parentheses straight A plus straight B close parentheses jika straight A equals straight B equals 1 third straight pi .

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses straight A plus straight B close parentheses end cell equals cell fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A times tan space straight B end fraction end cell row blank equals cell fraction numerator tan space open parentheses begin display style 1 third end style straight pi close parentheses plus tan space open parentheses 1 third straight pi close parentheses over denominator 1 minus tan space open parentheses 1 third straight pi close parentheses times tan space open parentheses 1 third straight pi close parentheses end fraction end cell row blank equals cell fraction numerator 2 space tan space open parentheses begin display style 1 third straight pi end style close parentheses over denominator 1 minus tan squared space open parentheses 1 third straight pi close parentheses end fraction end cell row blank equals cell fraction numerator 2 space tan space straight A over denominator 1 minus tan squared space straight A end fraction end cell row blank equals cell tan space 2 straight A end cell end table$

atau

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses straight A plus straight B close parentheses end cell equals cell fraction numerator tan space straight A plus tan space straight B over denominator 1 minus tan space straight A times tan space straight B end fraction end cell row blank equals cell fraction numerator tan space open parentheses begin display style 1 third straight pi end style close parentheses plus tan space open parentheses 1 third straight pi close parentheses over denominator 1 minus tan space open parentheses 1 third straight pi close parentheses times tan space open parentheses 1 third straight pi close parentheses end fraction end cell row blank equals cell fraction numerator 2 space tan space open parentheses begin display style 1 third straight pi end style close parentheses over denominator 1 minus tan squared space open parentheses 1 third straight pi close parentheses end fraction end cell row blank equals cell fraction numerator 2 space tan space straight B over denominator 1 minus tan squared space straight B end fraction end cell row blank equals cell tan space 2 straight B end cell end table$

Jadi, jika straight A equals straight B equals 1 third straight pi berlaku rumus tan space open parentheses straight A plus straight B close parentheses sehingga menghasilkan rumus baru yaitu tan space 2 straight A atau tan space 2 straight B .