Pertanyaan

Buktikan: a. sin x 1 − cos x = tan 2 x

Buktikan:

a. $\frac{1 - cos x}{sin x} = tan \frac{x}{2}$ $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator 1 minus cos space x over denominator sin space x end fraction equals tan space x over 2$ .

Pembahasan

Perkalian Bentuk Aljabar Identitas Trigonometri Sudut Paruhpada Tangen Akan dibuktikan . Kita buktikan dari ruas kanan ke ruas kiri. Bukti: Dengan menggunakan rumus sudut paruhpada tangen, maka: Terbukti! Jadi, terbukti bahwa .

Perkalian Bentuk Aljabar

Identitas Trigonometri

table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space alpha plus cos squared space alpha end cell equals 1 row cell sin squared space alpha end cell equals cell 1 minus cos squared space alpha end cell row cell cos squared space alpha end cell equals cell 1 minus sin squared space alpha end cell end table

Sudut Paruh pada Tangen

$tan space 1 half alpha equals square root of fraction numerator 1 minus cos space alpha over denominator 1 plus cos space alpha end fraction end root$

Akan dibuktikan $fraction numerator 1 minus cos space x over denominator sin space x end fraction equals tan space x over 2$ .

Kita buktikan dari ruas kanan ke ruas kiri.

Bukti:

Dengan menggunakan rumus sudut paruh pada tangen, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x over 2 end cell equals cell square root of fraction numerator 1 minus cos space x over denominator 1 plus cos space x end fraction end root end cell row blank equals cell square root of fraction numerator 1 minus cos space x over denominator 1 plus cos space x end fraction cross times fraction numerator 1 minus cos space x over denominator 1 minus cos space x end fraction end root end cell row blank equals cell square root of fraction numerator open parentheses 1 minus cos space x close parentheses squared over denominator 1 squared minus cos squared space x end fraction end root end cell row blank equals cell square root of fraction numerator open parentheses 1 minus cos space x close parentheses squared over denominator 1 minus cos squared space x end fraction end root end cell row blank equals cell square root of fraction numerator open parentheses 1 minus cos space x close parentheses squared over denominator sin squared space x end fraction end root end cell row blank equals cell fraction numerator 1 minus cos space x over denominator sin space x end fraction end cell end table$

Terbukti!

Jadi, terbukti bahwa $fraction numerator 1 minus cos space x over denominator sin space x end fraction equals tan space x over 2$ .