Buktikan identitas trigonometri berikut. e. 1+cos θsin θ+tan θ=tan θ

Pertanyaan

Buktikan identitas trigonometri berikut.

e. $fraction numerator sin space theta plus tan space theta over denominator 1 plus cos space theta end fraction equals tan space theta$

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

terbukti bahwa $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space theta plus tan space theta over denominator 1 plus cos space theta end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank theta end table$ .

Pembahasan

Ingat!

$tan space theta equals fraction numerator sin space theta over denominator cos space theta end fraction$

Akan dibuktikan

$fraction numerator sin space theta plus tan space theta over denominator 1 plus cos space theta end fraction equals tan space theta$

Perhatikan perhitungan berikut

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space theta plus tan space theta over denominator 1 plus cos space theta end fraction end cell equals cell fraction numerator 1 plus begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style over denominator 1 plus cos space theta end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator sin space theta times cos space theta plus sin space theta over denominator cos space theta end fraction end style over denominator 1 plus cos space theta end fraction end cell row blank equals cell fraction numerator sin space theta times cos space theta plus sin space theta over denominator cos space theta end fraction times fraction numerator begin display style 1 end style over denominator 1 plus cos space theta end fraction end cell row blank equals cell fraction numerator sin space theta up diagonal strike open parentheses 1 plus cos space theta close parentheses end strike over denominator cos space theta end fraction times fraction numerator begin display style 1 end style over denominator up diagonal strike 1 plus cos space theta end strike end fraction end cell row blank equals cell fraction numerator sin space theta over denominator cos space theta end fraction end cell row blank equals cell tan space theta end cell end table$

Dengan demikian terbukti bahwa $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space theta plus tan space theta over denominator 1 plus cos space theta end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank theta end table$ .