Buktikan identitas trigonometri berikut. tan θ−csc θ sec θ(1−2 cos2 θ)=cot θ

Pertanyaan

Buktikan identitas trigonometri berikut.

tan space theta minus csc space theta space sec space theta open parentheses 1 minus 2 space cos squared space theta close parentheses equals cot space theta

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

terbukti bahwa tan space theta minus csc space theta space sec space theta open parentheses 1 minus 2 space cos squared space theta close parentheses equals cot space theta.

Pembahasan

Ingat kembali identitas dasar trigonometri berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space theta end cell equals cell fraction numerator sin space theta space over denominator cos space theta end fraction end cell row cell csc space theta end cell equals cell fraction numerator 1 over denominator sin space theta end fraction end cell row cell sec space theta end cell equals cell fraction numerator 1 over denominator cos space theta space 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 tan space theta minus csc space theta space sec space theta open parentheses 1 minus 2 space c os squared space theta close parentheses end cell equals cell cot space theta end cell row cell fraction numerator sin space theta over denominator cos space theta end fraction minus fraction numerator 1 space over denominator sin space theta end fraction times fraction numerator 1 over denominator cos space theta end fraction open parentheses 1 minus 2 space cos squared space theta close parentheses end cell equals cell cot space theta end cell row cell fraction numerator sin space theta squared minus 1 minus 2 space cos squared space theta over denominator cos space theta space sin space theta end fraction end cell equals cell cot space theta end cell row cell fraction numerator sin space theta squared minus 1 plus cos space theta squared plus space cos space theta squared over denominator cos space theta space sin space theta end fraction end cell equals cell cot space theta end cell row cell fraction numerator 1 minus 1 plus cos space theta squared over denominator cos space theta space sin space theta end fraction end cell equals cell cot space theta end cell row cell fraction numerator cos space theta squared over denominator cos space theta squared space sin space theta end fraction end cell equals cell cot space theta end cell row cell fraction numerator cos space theta over denominator sin space theta end fraction end cell equals cell cot space theta end cell row cell cot space theta end cell equals cell cot space theta end cell row blank blank blank end table

Jadi, terbukti bahwa tan space theta minus csc space theta space sec space theta open parentheses 1 minus 2 space cos squared space theta close parentheses equals cot space theta.

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