Pertanyaan

Nyatakan dalam tan x setiap bentuk ekspresi berikut. a. tan ( 3 1 π + x )

Nyatakan dalam $tan x$ setiap bentuk ekspresi berikut.

a. $tan (\frac{1}{3} π + x)$

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

.

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses 1 third straight pi plus straight x close parentheses end cell equals cell fraction numerator 1 plus square root of 3 space tan space x over denominator square root of 3 minus tan space x end fraction end cell end table$ .

Pembahasan

Ingat rumus jumlah sudut pada tangen : Berdasarkan rumus tersebut, maka: Jadi, .

Ingat rumus jumlah sudut pada tangen :

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space left parenthesis A plus B right parenthesis end cell equals cell fraction numerator tan space A plus tan space B over denominator 1 minus tan space A space tan space B end fraction end cell end table$

Berdasarkan rumus tersebut, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses 1 third straight pi plus straight x close parentheses end cell equals cell fraction numerator tan space 1 third straight pi plus tan space straight x over denominator 1 minus tan space 1 third straight pi space tan space straight x end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 over denominator square root of 3 end fraction end style plus tan space x over denominator 1 minus begin display style fraction numerator 1 over denominator square root of 3 end fraction end style space tan space x end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 over denominator square root of 3 end fraction plus tan space x end style over denominator 1 minus begin display style fraction numerator 1 over denominator square root of 3 end fraction end style space tan space x end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus square root of 3 space tan space x over denominator square root of 3 minus tan space x end fraction end cell end table$

Jadi, $table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses 1 third straight pi plus straight x close parentheses end cell equals cell fraction numerator 1 plus square root of 3 space tan space x over denominator square root of 3 minus tan space x end fraction end cell end table$ .