Jika tan x=21, tan y=31, x dan y merupakan sudut lancip, hitunglah: d. tan (x+2y)

Pertanyaan

Jika $\tan\;x=\frac12$ , $\tan\;y=\frac13$ , $x$ dan $y$ merupakan sudut lancip, hitunglah:

d. $\tan\;\left(x+2y\right)$ $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x plus 2 y close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table

Pembahasan

Sudut Rangkap pada Tangen

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

Jumlah Dua Sudut pada Tangen

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

Diketahui tan space x equals 1 half , tan space y equals 1 third , dan merupakan sudut lancip (terletak di kuadran I), maka hasil dari tan space open parentheses x plus 2 y close parentheses adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses x plus 2 y close parentheses end cell equals cell fraction numerator tan space x plus tan space 2 y over denominator 1 minus tan space x space tan space 2 y end fraction end cell row blank equals cell fraction numerator begin display style tan space x plus fraction numerator 2 space tan space y over denominator 1 minus tan squared space y end fraction end style over denominator 1 minus open parentheses tan space x times fraction numerator 2 space tan space y over denominator 1 minus tan squared space y end fraction close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus fraction numerator 2 times begin display style 1 third end style over denominator 1 minus open parentheses begin display style 1 third end style close parentheses squared end fraction end style over denominator 1 minus open parentheses 1 half times fraction numerator 2 times begin display style 1 third end style over denominator 1 minus open parentheses begin display style 1 third end style close parentheses squared end fraction close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 half plus fraction numerator begin display style 2 over 3 end style over denominator begin display style 8 over 9 end style end fraction end style over denominator 1 minus open parentheses 1 half times fraction numerator begin display style 2 over 3 end style over denominator begin display style 8 over 9 end style end fraction close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus open parentheses begin display style 2 over 3 end style times begin display style 9 over 8 end style close parentheses over denominator 1 minus open parentheses begin display style fraction numerator 1 over denominator up diagonal strike 2 end fraction end style times fraction numerator up diagonal strike 2 over denominator 3 end fraction times 9 over 8 close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style plus begin display style 3 over 4 end style over denominator 1 minus begin display style 3 over 8 end style end fraction end cell row blank equals cell fraction numerator begin display style 5 over 4 end style over denominator begin display style 5 over 8 end style end fraction end cell row blank equals cell fraction numerator up diagonal strike 5 over denominator 4 end fraction times fraction numerator 8 over denominator up diagonal strike 5 end fraction end cell row blank equals 2 row blank equals 2 end table$

Jadi, .