RoboguruRoboguru
SD

Jika tan(2x+45∘)=a,tan(x+30∘)=b,dan a⋅b∈{1,−1,2​,−2​},maka tan(3x+75∘)⋅tan(x+15∘)=…

Pertanyaan

Jika tan left parenthesis 2 x plus 45 degree right parenthesis equals a comma tan left parenthesis x plus 30 degree right parenthesis equals b commadan a times b not an element of open curly brackets 1 comma negative 1 comma square root of 2 comma negative square root of 2 close curly brackets commamaka tan open parentheses 3 x plus 75 degree close parentheses times tan open parentheses x plus 15 degree close parentheses equals horizontal ellipsis

  1. fraction numerator a squared minus b squared over denominator 1 plus a squared b squared end fraction 

  2. fraction numerator a squared plus b squared over denominator 1 minus a squared b squared end fraction    

  3. fraction numerator a squared minus b squared over denominator 1 minus a squared b squared end fraction   

  4. fraction numerator a squared minus b squared over denominator 1 minus 2 a squared b squared end fraction  

  5. fraction numerator a squared plus b squared over denominator 1 plus 2 a squared b squared end fraction     

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C

Pembahasan

Ingat bahwa :

rumus jumlah atau selisih  dua sudut tan

tan open parentheses A plus-or-minus B close parentheses equals fraction numerator tan space A plus-or-minus tan space B over denominator 1 minus-or-plus space tan space A space tan space B end fraction

Sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses 3 x minus 30 degree close parentheses end cell equals cell tan space open parentheses open parentheses 2 x minus 45 close parentheses plus open parentheses x plus 15 degree close parentheses close parentheses end cell row blank equals cell fraction numerator tan open parentheses 2 x minus 45 close parentheses plus tan open parentheses x plus 15 degree close parentheses over denominator 1 minus tan space open parentheses 2 x minus 45 close parentheses times tan space open parentheses x plus 15 degree close parentheses end fraction end cell row blank equals cell fraction numerator a plus b over denominator 1 minus a times b end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses x minus 60 degree close parentheses end cell equals cell tan space open parentheses open parentheses 2 x minus 45 close parentheses minus open parentheses x plus 15 degree close parentheses close parentheses end cell row blank equals cell fraction numerator tan open parentheses 2 x minus 45 close parentheses minus tan open parentheses x plus 15 degree close parentheses over denominator 1 plus tan space open parentheses 2 x minus 45 close parentheses times tan space open parentheses x plus 15 degree close parentheses end fraction end cell row blank equals cell fraction numerator a minus b over denominator 1 plus a times b end fraction end cell end table

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell tan open parentheses 3 x plus 75 degree close parentheses times tan open parentheses x plus 15 degree close parentheses end cell equals cell open parentheses fraction numerator a plus b over denominator 1 minus a b end fraction close parentheses open parentheses fraction numerator a minus b over denominator 1 plus a b end fraction close parentheses end cell row blank equals cell fraction numerator a squared minus b squared over denominator 1 minus a squared b squared end fraction end cell end table

Jadi, jawaban yang tepat adalah C

27

5.0 (1 rating)

Pertanyaan serupa

Jika tan α tan β=1, maka tan (α+β)tan (α−β)​ sama dengan ...

52

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia