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Buktikan identitas trigonometri berikut. cot θ+1+cos θsin θ​=csc θ

Pertanyaan

Buktikan identitas trigonometri berikut.

cot space theta plus fraction numerator sin space theta over denominator 1 plus cos space theta end fraction equals csc space theta

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

terbukti bahwa cot space theta plus fraction numerator sin space theta over denominator 1 plus cos space theta end fraction equals csc space theta.

Pembahasan

Ingat kembali identitas dasar trigonometri berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared space theta plus cos squared space theta end cell equals 1 row cell csc space theta end cell equals cell fraction numerator 1 over denominator sin space theta end fraction end cell end table

Maka, pembuktian dari identitas trigonometri berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row cell cot space theta plus fraction numerator sin space theta over denominator 1 plus cos space theta end fraction end cell equals cell csc space theta end cell row cell fraction numerator cos space theta over denominator sin space theta end fraction plus fraction numerator sin space theta over denominator 1 plus cos space theta end fraction end cell equals cell csc space theta end cell row cell fraction numerator open parentheses 1 plus cos space theta close parentheses open parentheses cos space theta plus sin space theta squared close parentheses over denominator open parentheses 1 plus cos space theta close parentheses space sin space theta end fraction end cell equals cell csc space theta end cell row cell fraction numerator cos space theta plus cos space theta squared plus sin space theta squared over denominator open parentheses 1 plus cos space theta close parentheses space sin space theta end fraction end cell equals cell csc space theta end cell row cell fraction numerator cos space theta plus 1 over denominator 1 plus cos space theta space sin space theta end fraction end cell equals cell csc space theta end cell row cell fraction numerator 1 over denominator sin space theta end fraction end cell equals cell csc space theta end cell row cell csc space theta end cell equals cell csc space theta space open parentheses Terbukti close parentheses end cell end table

Jadi, terbukti bahwa cot space theta plus fraction numerator sin space theta over denominator 1 plus cos space theta end fraction equals csc space theta.

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