RoboguruRoboguru
SD

Nilai dari sin 70∘−sin 20∘cos 20∘−cos 70∘​ adalah ... .

Pertanyaan

Nilai dari fraction numerator cos space 20 degree minus cos space 70 degree over denominator sin space 70 degree minus sin space 20 degree end fraction adalah ... .

  1. 2

  2. 1

  3. 0

  4. 1 half

  5. fraction numerator 1 over denominator square root of 2 end fraction

L. Nikmah

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Ingat rumus jumlah dan selisih trigonometri berikut ini:

cos space A minus cos space B equals negative 2 space sin space 1 half open parentheses A plus B close parentheses space sin space 1 half open parentheses A minus B close parentheses

sin space A minus sin space B equals 2 space cos space 1 half open parentheses A plus B close parentheses space sin space 1 half open parentheses A minus B close parentheses

Dengan menggunakan konsep di atas, diperoleh hasil:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space 20 degree space minus space cos space 70 degree over denominator sin space 70 degree space minus space sin space 20 degree end fraction end cell equals cell fraction numerator negative 2 space sin space begin display style 1 half end style open parentheses 20 degree plus 70 degree close parentheses space sin space 1 half open parentheses 20 degree minus 70 degree close parentheses over denominator 2 space cos space 1 half open parentheses 70 degree plus 20 degree close parentheses space sin space 1 half open parentheses 70 degree minus space 20 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative 2 space sin space begin display style 1 half end style open parentheses 90 degree close parentheses space sin space 1 half open parentheses negative 50 degree close parentheses over denominator 2 space cos space 1 half open parentheses 90 degree close parentheses space sin space 1 half open parentheses 50 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative 2 space sin space 45 degree space sin space open parentheses negative 25 degree close parentheses over denominator 2 space cos space 45 degree space sin space 25 degree end fraction end cell row blank equals cell fraction numerator negative 2 space sin space 45 degree space open parentheses negative sin space 25 degree close parentheses over denominator 2 space cos space 45 degree space sin space 25 degree end fraction end cell row blank equals cell fraction numerator 2 space sin space 45 degree space sin space 25 degree over denominator 2 space cos space 45 degree space sin space 25 degree end fraction end cell row blank equals cell fraction numerator sin space 45 degree over denominator cos space 45 degree end fraction end cell row blank equals cell tan space 45 degree end cell row blank equals 1 end table

Jadi, fraction numerator cos space 20 degree minus cos space 70 degree over denominator sin space 70 degree minus sin space 20 degree end fraction equals 1.

Oleh karena itu, jawaban yang benar adalah B.

94

4.5 (4 rating)

Pertanyaan serupa

Nilai dari cos105∘−cos15∘sin105∘−sin15∘​ = ...

366

3.6

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