3. Buktikanlah identitas-identitas trigonometri berikut. c. 1− cos Asin2 A=1+cos A

Pertanyaan

3. Buktikanlah identitas-identitas trigonometri berikut.

c. $fraction numerator sin squared space A over denominator 1 minus space cos space A end fraction equals 1 plus cos space A$

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

terbukti bahwa $fraction numerator sin squared space A over denominator 1 minus space cos space A end fraction equals 1 plus cos space A$ .

Pembahasan

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

table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space A plus cos squared space A end cell equals 1 row cell sin squared space A end cell equals cell 1 minus cos squared space A end cell end table

Sehingga diperoleh:

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

Dengan demikian, terbukti bahwa $fraction numerator sin squared space A over denominator 1 minus space cos space A end fraction equals 1 plus cos space A$ .