3. Buktikanlah identitas-identitas trigonometri berikut. i. cos A2−sin2 A=secan A+cos A

Pertanyaan

3. Buktikanlah identitas-identitas trigonometri berikut.

i. $fraction numerator 2 minus sin squared space A over denominator cos space A end fraction equals secan space A plus cos space A$

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Pembahasan

Untuk membuktikan persamaan tersebut, kita akan menyederhanakan persamaan di ruas kanan untuk mendapatkan persamaan di ruas kiri, kemudian ingat kembali identitas trigonometri berikut.

$secan space A equals fraction numerator 1 over denominator cos space A end fraction$

Sehingga diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 minus sin squared space A over denominator cos space A end fraction end cell equals cell secan space A plus cos space A end cell row cell fraction numerator 2 minus sin squared space A over denominator cos space A end fraction end cell equals cell fraction numerator 1 over denominator cos space A end fraction plus cos space A end cell row cell fraction numerator 2 minus sin squared space A over denominator cos space A end fraction end cell equals cell fraction numerator 1 plus cos squared A over denominator cos space A end fraction end cell row cell fraction numerator 2 minus sin squared space A over denominator cos space A end fraction end cell equals cell fraction numerator 1 plus open parentheses 1 minus sin squared space A close parentheses over denominator cos space A end fraction end cell row cell fraction numerator 2 minus sin squared space A over denominator cos space A end fraction end cell equals cell fraction numerator 2 minus sin squared space A over denominator cos space A end fraction space begin bold style left parenthesis terbukti right parenthesis end style end cell end table$

Dengan demikian, terbukti bahwa :

$fraction numerator 2 minus sin squared space A over denominator cos space A end fraction equals secan space A plus cos space A$ .