RoboguruRoboguru
SD

4. Tunjukkan kebenaran identitas trigonometri berikut. c. cosec A−cotan A1​=cosec A+cotan A

Pertanyaan

4. Tunjukkan kebenaran identitas trigonometri berikut.

c. fraction numerator 1 over denominator cosec space A minus cotan space A end fraction equals cosec space A plus cotan space A 

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Untuk membuktikan persamaan tersebut, kita akan menyederhanakan persamaan di ruas kiri untuk mendapatkan persamaan di ruas kanan, kemudian ingat kembali identitas trigonometri berikut.

  • cosec space x equals fraction numerator 1 over denominator sin space x end fraction 
  • cotan space x equals fraction numerator cos space x over denominator sin space x end fraction 
  • table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space x plus cos squared space x end cell equals 1 row cell cos squared space x end cell equals cell 1 minus sin squared space x end cell end table 

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 over denominator cosec space A minus cotan space A end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator sin space A end fraction end style minus begin display style fraction numerator cos space A over denominator sin space A end fraction end style end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator 1 over denominator begin display style fraction numerator 1 minus cos space A over denominator sin space A end fraction end style end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator sin space A over denominator 1 minus cos space A end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator sin space A over denominator 1 minus cos space A end fraction cross times fraction numerator 1 plus cos space A over denominator 1 plus cos space A end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator sin space A open parentheses 1 plus cos space A close parentheses over denominator 1 minus cos squared space A end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator sin space A open parentheses 1 plus cos space A close parentheses over denominator 1 minus open parentheses 1 minus sin squared space A close parentheses end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator up diagonal strike sin space A end strike open parentheses 1 plus cos space A close parentheses over denominator sin to the power of up diagonal strike 2 end exponent space A end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator 1 plus cos space A over denominator sin space A end fraction end cell equals cell cosec space A plus cotan space A end cell row cell fraction numerator 1 over denominator sin space A end fraction plus fraction numerator cos space A over denominator sin space A end fraction end cell equals cell cosec space A plus cotan space A end cell row cell cosec space A plus cotan space A end cell equals cell cosec space A plus cotan space A space begin bold style left parenthesis terbukti right parenthesis end style end cell row blank blank blank end table 

Dengan demikian, terbukti bahwa :

fraction numerator 1 over denominator cosec space A minus cotan space A end fraction equals cosec space A plus cotan space A

89

5.0 (2 rating)

Pertanyaan serupa

3. Buktikanlah identitas-identitas trigonometri berikut. j. cosec A+tan A+cotan A=sin A cos Acos A+1​

182

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