Pertanyaan

Buktikan identitas trigonometri berikut. ( 1 − cos x ) ( 1 + cos x ) ( 1 + cotan 2 x ) = 1

Buktikan identitas trigonometri berikut.

$(1 - cos x) (1 + cos x) (1 + cotan^{2} x) = 1$

N. Putri

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Berikut ini adalah pembuktian identitas trogonometrinya. Dengan begitu terbukti identitas trigonometri pada soal tersebut.

Berikut ini adalah pembuktian identitas trogonometrinya.

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 1 minus cos space x right parenthesis left parenthesis 1 plus cos space x right parenthesis left parenthesis 1 plus c o tan squared x right parenthesis end cell equals 1 row cell left parenthesis 1 minus cos squared x right parenthesis left parenthesis 1 plus c o tan squared x right parenthesis end cell equals 1 row cell 1 minus cos squared x plus c o tan squared x minus cos squared x space c o tan squared x end cell equals 1 row cell negative cos squared x plus fraction numerator cos squared x over denominator sin squared x end fraction minus cos squared x fraction numerator cos squared x over denominator sin squared x end fraction end cell equals 0 row cell fraction numerator negative sin squared x space cos squared x plus cos squared x minus cos to the power of 4 x over denominator sin squared x end fraction end cell equals 0 row cell negative sin squared x space cos squared x plus cos squared x minus cos to the power of 4 x end cell equals 0 row cell negative sin squared x plus 1 minus cos squared x end cell equals 0 row cell cos squared x plus sin squared x end cell equals 1 end table end style$

Dengan begitu terbukti identitas trigonometri pada soal tersebut.