Pertanyaan

tan ( 4 1 π − α ) = ...

$tan (\frac{1}{4} π - α) =$ ...

$fraction numerator cos space alpha minus sin space alpha over denominator cos space alpha plus sin space alpha end fraction$
$fraction numerator sin space alpha plus cos space alpha over denominator cos space alpha minus sin space alpha end fraction$

R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Rumus tangen selisih dua sudut yaitu: Kemudian ingatlah bahwa , sehingga diperoleh penyelesaiannya yaitu: Jadi, . Oleh karena itu, jawaban yang benar adalah A.

Rumus tangen selisih dua sudut yaitu:

$tan space open parentheses alpha minus beta close parentheses equals fraction numerator tan space alpha minus tan space beta over denominator 1 plus tan space alpha times tan space beta end fraction$

Kemudian ingatlah bahwa straight pi equals 180 degree , sehingga diperoleh penyelesaiannya yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses 1 fourth straight pi minus alpha close parentheses end cell equals cell tan space open parentheses 1 fourth times 180 degree minus alpha close parentheses end cell row blank equals cell tan space open parentheses 45 degree minus alpha close parentheses end cell row blank equals cell fraction numerator tan space 45 degree minus tan space alpha over denominator 1 plus tan space 45 times tan space alpha end fraction end cell row blank equals cell fraction numerator 1 minus tan space alpha over denominator 1 plus 1 times tan space alpha end fraction end cell row blank equals cell fraction numerator 1 minus tan space alpha over denominator 1 plus tan space alpha end fraction end cell row blank equals cell fraction numerator 1 minus begin display style fraction numerator sin space alpha over denominator cos space alpha end fraction end style over denominator 1 plus begin display style fraction numerator sin space alpha over denominator cos space alpha end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator cos space alpha over denominator cos space alpha end fraction end style minus begin display style fraction numerator sin space alpha over denominator cos space alpha end fraction end style over denominator begin display style fraction numerator cos space alpha over denominator cos space alpha end fraction end style plus begin display style fraction numerator sin space alpha over denominator cos space alpha end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator cos space alpha minus sin space alpha over denominator up diagonal strike cos space alpha end strike end fraction end style over denominator begin display style fraction numerator cos space alpha plus sin space alpha over denominator up diagonal strike cos space alpha end strike end fraction end style end fraction end cell row blank equals cell fraction numerator cos space alpha minus sin space alpha over denominator cos space alpha plus sin space alpha end fraction end cell end table$

Jadi, tan space open parentheses 1 fourth straight pi minus alpha close parentheses equals $fraction numerator cos space alpha minus sin space alpha over denominator cos space alpha plus sin space alpha end fraction$ .

Oleh karena itu, jawaban yang benar adalah A.