Pertanyaan

Buktikan identitas berikut ini. sin A + sec A tan 2 A + cos 2 A = sec A − sin A

Buktikan identitas berikut ini.

$\frac{tan ^{2} A + cos ^{2} A}{sin A + sec A} = sec A - sin A$

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan menggunakan konsep identitas trigonometri, Jadi, terbukti bahwa .

Dengan menggunakan konsep identitas trigonometri,

$begin mathsize 11px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator tan squared A plus cos squared A over denominator sin space A plus sec space A end fraction end cell equals cell fraction numerator open parentheses sec squared A minus 1 close parentheses plus open parentheses 1 minus sin squared A close parentheses over denominator sin space A plus sec space A end fraction end cell row blank equals cell fraction numerator sec squared A minus sin squared A over denominator sin space A plus sec space A end fraction end cell row blank equals cell fraction numerator open parentheses sec space A minus sin space A close parentheses open parentheses sec space A plus sin space A close parentheses over denominator sin space A plus sec space A end fraction end cell row blank equals cell sec space A minus sin space A end cell end table end style$

Jadi, terbukti bahwa

$begin mathsize 14px style fraction numerator tan squared A plus cos squared A over denominator sin space A plus sec space A end fraction equals sec space A minus sin space A end style$ .