Pertanyaan

Bentuk tan x − sec x +1 tan x + sec x- 1

Bentuk $\frac{tan x + sec x - 1}{tan x - sec x +1}$

$begin mathsize 14px style fraction numerator 1 minus sin space x over denominator cos space x space end fraction end style$
$begin mathsize 14px style fraction numerator sin space x minus 1 over denominator cos space x space end fraction end style$
$fraction numerator size 14px sin size 14px space size 14px x size 14px plus size 14px 1 over denominator size 14px cos size 14px space size 14px x size 14px space end fraction$
$begin mathsize 14px style fraction numerator cos space x minus 1 over denominator sin space x space end fraction end style$
$begin mathsize 14px style fraction numerator cos space x plus 1 over denominator sin space x space end fraction end style$

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Habis dalam

Klaim

N. Putri

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Dari soal tersebut, dapati disederhanakan menjadi berikut ini: Dengan begitu, opsi jawaban yang tepat adalah C.

Dari soal tersebut, dapati disederhanakan menjadi berikut ini:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan space x plus s e c space x minus 1 over denominator tan space x minus s e c space x plus 1 end fraction end cell equals blank row cell fraction numerator begin display style fraction numerator sin space x over denominator cos space x end fraction end style plus begin display style fraction numerator 1 over denominator cos space x end fraction end style minus begin display style fraction numerator cos space x over denominator cos space x end fraction end style over denominator begin display style fraction numerator sin space x over denominator cos space x end fraction end style minus begin display style fraction numerator 1 over denominator cos space x end fraction end style plus begin display style fraction numerator cos space x over denominator cos space x end fraction end style end fraction end cell equals blank row cell fraction numerator sin space x space plus 1 minus cos space x over denominator sin space x minus 1 plus cos space x end fraction end cell equals blank row cell fraction numerator negative cos space x plus sin space x plus 1 over denominator cos space x plus sin space x minus 1 end fraction cross times fraction numerator left parenthesis cos space x plus sin space x right parenthesis plus 1 over denominator left parenthesis cos space x plus sin space x right parenthesis plus 1 end fraction end cell equals blank row cell fraction numerator sin squared x plus 2 sin space x plus 1 minus cos squared x over denominator cos squared plus 2 sin space x space cos space x plus sin squared x minus 1 end fraction end cell equals blank row cell fraction numerator sin squared x plus 2 sin space x plus sin squared x over denominator 2 sin space x space cos space x plus 1 minus 1 end fraction end cell equals blank row cell fraction numerator 2 sin squared x plus 2 sin space x over denominator 2 sin space x space cos space x end fraction end cell equals blank row cell fraction numerator sin space x plus 1 over denominator cos space x end fraction end cell equals blank end table end style$

Dengan begitu, opsi jawaban yang tepat adalah C.