Pertanyaan

Bentuk yang sama nilainya dengan sin x + cos x − 1 sin x − cos x + 1 adalah ...

Bentuk yang sama nilainya dengan $\frac{sin x - cos x + 1}{sin x + cos x - 1}$ adalah ...

$fraction numerator sin space x plus 1 over denominator cos space x end fraction$
$fraction numerator sec space x over denominator 1 plus cos space x end fraction$
$fraction numerator 1 plus sin space x over denominator 1 plus cos space x end fraction$
$fraction numerator cos space x over denominator 1 minus sin space x end fraction$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat! Bentuk yang sama nilainya dengan adalah: Sehingga, . Jadi, jawaban yang tepat adalah A.

Ingat!

sin squared space x plus cos squared space x equals 1

Bentuk yang sama nilainya dengan $fraction numerator sin space x minus cos space x plus 1 over denominator sin space x plus cos space x minus 1 end fraction$ adalah:

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

Sehingga, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space x minus cos space x plus 1 over denominator sin space x plus cos space x minus 1 end fraction end cell end table equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space x plus 1 over denominator cos space x end fraction end cell end table$ .

Jadi, jawaban yang tepat adalah A.