Pertanyaan

Jika tan x = 5 1 dan tan y = 4 1 ,maka nilai dari tan⁡(2x + 2y) adalah ....

Jika $tan x = \frac{1}{5}$ dan $tan y = \frac{1}{4}$ , maka nilai dari tan⁡(2x + 2y) adalah ....

tidak terdefinisi

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

M. Robo

Master Teacher

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Sehingga perlu dicari terlebih dahulu nilai dari tan ⁡2x dan tan⁡ 2y. Perhatikan bahwa Selanjutnya Sehingga

Perhatikan bahwa

$begin mathsize 14px style tan invisible function application open parentheses 2 x plus 2 y close parentheses equals fraction numerator tan invisible function application 2 x plus tan invisible function application 2 y over denominator 1 minus tan invisible function application 2 x tan invisible function application 2 y end fraction end style$

Sehingga perlu dicari terlebih dahulu nilai dari tan ⁡2x dan tan⁡ 2y.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 2 x end cell equals cell fraction numerator 2 tan invisible function application x over denominator 1 minus tan squared invisible function application x end fraction end cell row blank equals cell fraction numerator 2 open parentheses 1 fifth close parentheses over denominator 1 minus open parentheses 1 fifth close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 over 5 over denominator 1 minus 1 over 25 end fraction end cell row blank equals cell fraction numerator 2 over 5 over denominator 25 over 25 minus 1 over 25 end fraction end cell row blank equals cell fraction numerator 2 over 5 over denominator 24 over 25 end fraction end cell row blank equals cell 2 over 5 cross times 25 over 24 end cell row blank equals cell 1 over 1 cross times 5 over 12 end cell row blank equals cell 5 over 12 end cell end table end style$

Selanjutnya

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 2 y end cell equals cell fraction numerator 2 tan invisible function application y over denominator 1 minus tan squared invisible function application y end fraction end cell row blank equals cell fraction numerator 2 open parentheses 1 fourth close parentheses over denominator 1 minus open parentheses 1 fourth close parentheses squared end fraction end cell row blank equals cell fraction numerator 1 half over denominator 1 minus 1 over 16 end fraction end cell row blank equals cell fraction numerator 1 half over denominator 16 over 16 minus 1 over 16 end fraction end cell row blank equals cell fraction numerator 1 half over denominator 15 over 16 end fraction end cell row blank equals cell 1 half cross times 16 over 15 end cell row blank equals cell 1 over 1 cross times 8 over 15 end cell row blank equals cell 8 over 15 end cell end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application open parentheses 2 x plus 2 y close parentheses end cell equals cell fraction numerator tan invisible function application 2 x plus tan invisible function application 2 y over denominator 1 minus tan invisible function application 2 x tan invisible function application 2 y end fraction end cell row blank equals cell fraction numerator 5 over 12 plus 8 over 15 over denominator 1 minus 5 over 12 times 8 over 15 end fraction end cell row blank equals cell fraction numerator fraction numerator 5 times 5 over denominator 12 times 5 end fraction plus fraction numerator 8 times 4 over denominator 15 times 4 end fraction over denominator 1 minus 1 third times 2 over 3 end fraction end cell row blank equals cell fraction numerator 25 over 60 plus 32 over 60 over denominator 1 minus 2 over 9 end fraction equals fraction numerator 57 over 60 over denominator 7 over 9 end fraction end cell row blank equals cell 57 over 60 cross times 9 over 7 end cell row blank equals cell 57 over 20 cross times 3 over 7 end cell row blank equals cell 171 over 140 end cell end table end style$