Pertanyaan

Bentuk yang ekuivalen dengan cos A − sin A cos A + sin A − cos A + sin A cos A − sin A adalah ....

Bentuk yang ekuivalen dengan $\frac{cos A + sin A}{cos A - sin A} - \frac{cos A - sin A}{cos A + sin A}$ adalah ....

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat kembali: Maka: Jadi, jawaban yang benar adalah E.

Ingat kembali:

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 2 straight A end cell equals cell 2 space sin space straight A space cos space straight A end cell row cell cos space 2 straight A end cell equals cell cos squared space straight A minus sin squared space straight A end cell row blank equals cell 1 minus 2 space sin squared space straight A end cell row blank equals cell 2 space cos squared space straight A minus 1 end cell row cell fraction numerator sin space straight A over denominator cos space straight A end fraction end cell equals cell tan space straight A end cell end table$

Maka:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space straight A plus sin space straight A over denominator cos space straight A minus sin space straight A end fraction minus fraction numerator cos space straight A minus sin space straight A over denominator cos space straight A plus sin space straight A end fraction end cell equals cell fraction numerator open parentheses cos space straight A plus sin space straight A close parentheses squared minus open parentheses cos space straight A minus sin space straight A close parentheses squared over denominator open parentheses cos space straight A minus sin space straight A close parentheses open parentheses cos space straight A plus sin space straight A close parentheses end fraction end cell row blank equals cell fraction numerator open parentheses cos squared space straight A plus 2 space sin space straight A space cos space straight A plus sin squared space straight A close parentheses minus open parentheses cos squared space straight A minus 2 space sin space straight A space cos space straight A plus sin squared space straight A close parentheses over denominator cos squared space straight A up diagonal strike plus cos space straight A space sin space straight A end strike up diagonal strike negative sin space straight A space cos space straight A end strike minus sin squared space straight A end fraction end cell row blank equals cell fraction numerator up diagonal strike cos squared space straight A end strike plus 2 space sin space straight A space cos space straight A up diagonal strike plus sin squared space straight A end strike up diagonal strike negative cos squared space straight A end strike plus 2 space sin space straight A space cos space straight A up diagonal strike negative sin squared space straight A end strike over denominator cos squared space straight A minus sin squared space straight A end fraction end cell row blank equals cell fraction numerator 2 space sin space straight A space cos space straight A plus 2 space sin space straight A space cos space straight A over denominator cos space 2 straight A end fraction end cell row blank equals cell fraction numerator sin space 2 straight A plus sin space 2 straight A over denominator cos space 2 straight A end fraction end cell row blank equals cell fraction numerator 2 space sin space 2 straight A over denominator cos space 2 straight A end fraction end cell row blank equals cell 2 space tan space 2 straight A end cell end table end style$

Jadi, jawaban yang benar adalah E.