Pertanyaan

Jika sin ( A − 4 π ) − cos ( A − 4 π ) = 0 , maka tan A = ...

Jika $sin (A - \frac{π}{4}) - cos (A - \frac{π}{4}) = 0$ , maka tan A = ...

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Klaim

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Pembahasan

$sin space open parentheses A minus straight pi over 4 close parentheses minus 5 space cos open parentheses A minus straight pi over 4 close parentheses equals 0 sin space open parentheses A minus straight pi over 4 close parentheses equals 5 space cos open parentheses A minus straight pi over 4 close parentheses fraction numerator sin space open parentheses A minus straight pi over 4 close parentheses over denominator cos open parentheses A minus straight pi over 4 close parentheses end fraction equals 5 fraction numerator sin space A over denominator cos space A end fraction equals tan space A fraction numerator sin space open parentheses A minus straight pi over 4 close parentheses over denominator cos open parentheses A minus straight pi over 4 close parentheses end fraction equals 5 tan open parentheses A minus straight pi over 4 close parentheses equals 5 tan space left parenthesis A minus B right parenthesis space equals fraction numerator tan space A minus tan space B over denominator 1 plus tan space A space tan space B end fraction fraction numerator tan space A minus tan begin display style straight pi over 4 end style over denominator 1 plus tan space A space tan space begin display style straight pi over 4 end style end fraction equals 5 tan space A minus tan space straight pi over 4 equals 5 open parentheses 1 plus tan space A space tan space straight pi over 4 close parentheses tan space A minus 1 equals 5 left parenthesis 1 plus tan A right parenthesis tan space A minus 1 equals 5 plus 5 space tan space A 5 space tan space A minus tan space A equals negative 5 minus 1 4 space tan space A equals negative 6 tan space A equals negative 6 over 4 equals negative 3 over 2$