Roboguru

Nilai dari  ....

Pertanyaan

Nilai dari begin mathsize 14px style tan end style begin mathsize 14px style 45 degree end stylebegin mathsize 14px style equals end style....

  1. begin mathsize 14px style 2 plus square root of 3 end style 

  2. begin mathsize 14px style 2 minus square root of 3 end style 

  3. begin mathsize 14px style 1 fourth open parentheses square root of 6 minus square root of 2 close parentheses end style 

  4. begin mathsize 14px style 1 fourth open parentheses square root of 2 minus square root of 6 close parentheses end style 

  5. begin mathsize 14px style negative 1 fourth open parentheses square root of 2 plus square root of 6 close parentheses end style 

Pembahasan Soal:

Rumus jumlah dua sudut

begin mathsize 14px style 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 a degree plus b degree 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 cell fraction numerator tan space a degree plus tan space b degree over denominator 1 minus tan space a degree times tan space b degree end fraction end cell end table end style 

 Dalam hal ini, sudut a dan b merupakan sudut-sudut istimewa. Perhatikan bahwa sudut 75° dapat diperoleh dari jumlah dua sudut istimewa seperti yang berikut ini.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 75 degree end cell equals cell tan space open parentheses 45 degree plus 30 degree close parentheses end cell row blank equals cell fraction numerator tan space 45 degree plus tan space 30 degree over denominator 1 minus tan space 45 degree times tan space 30 degree end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 1 third end style square root of 3 over denominator 1 minus open parentheses 1 close parentheses open parentheses 1 third square root of 3 close parentheses end fraction end cell row blank equals cell fraction numerator 1 plus 1 third square root of 3 over denominator 1 minus 1 third square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus 1 third square root of 3 over denominator 1 minus 1 third square root of 3 end fraction times fraction numerator 1 plus 1 third square root of 3 over denominator 1 plus 1 third square root of 3 end fraction end cell row blank equals cell fraction numerator 1 plus begin display style 2 over 3 end style square root of 3 plus begin display style 1 third end style over denominator 1 minus 1 third end fraction end cell row blank equals cell fraction numerator begin display style 4 over 3 end style plus begin display style 2 over 3 end style square root of 3 over denominator begin display style 2 over 3 end style end fraction end cell row blank equals cell fraction numerator begin display style 2 over 3 end style open parentheses 2 plus square root of 3 close parentheses over denominator begin display style 2 over 3 end style end fraction end cell row blank equals cell 2 plus square root of 3 end cell end table end style

Jadi, Tan begin mathsize 14px style 75 degree end stylebegin mathsize 14px style equals end style begin mathsize 14px style 2 plus square root of 3 end style

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 15 Maret 2021

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved