Pertanyaan

Tunjukkan bahwa: cos 3 α + cos α sin 3 α + sin α = tan 2 α

Tunjukkan bahwa: $\frac{sin 3 α + sin α}{cos 3 α + cos α} = tan 2 α$

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

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$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 3 alpha plus sin space alpha over denominator cos space 3 alpha plus cos space alpha end fraction end cell equals cell tan space 2 alpha end cell row cell fraction numerator 2 times sin begin display style 1 half end style open parentheses 3 alpha plus alpha close parentheses times cos begin display style 1 half end style open parentheses 3 alpha minus alpha close parentheses over denominator 2 times cos 1 half open parentheses 3 alpha plus alpha close parentheses times cos 1 half open parentheses 3 alpha minus alpha close parentheses end fraction end cell equals cell tan space 2 alpha end cell row cell fraction numerator 2 times sin space 2 alpha times cos space alpha over denominator 2 times cos space 2 alpha times cos space alpha end fraction end cell equals cell tan space 2 alpha end cell row cell fraction numerator up diagonal strike 2 times sin space 2 alpha times up diagonal strike cos space alpha end strike over denominator up diagonal strike 2 times cos space 2 alpha times up diagonal strike cos space alpha end strike end fraction end cell equals cell tan space 2 alpha end cell row cell fraction numerator sin space 2 alpha over denominator cos space 2 alpha end fraction end cell equals cell tan space 2 alpha end cell row cell tan space 2 alpha end cell equals cell tan space 2 alpha end cell end table$

Terbukti bahwa identitas di atas benar.