Pertanyaan

Tunjukkan kebenaran identitas trigonometri berikut. d. 1 − cotan x 1 + cotan x = tan x − 1 1 + tan x

Tunjukkan kebenaran identitas trigonometri berikut.

d. $\frac{1 + cotan x}{1 - cotan x} = \frac{1 + tan x}{tan x - 1}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator 1 plus space cotan space x over denominator 1 space minus space cotan space x space end fraction equals fraction numerator 1 plus tan space x over denominator tan space x space minus 1 end fraction$ .

Pembahasan

Ingat! Akan ditunjukkan bahwa Perhatikan perhitungan berikut Dengan demikian terbukti bahwa .

Ingat!

$cotan space x equals fraction numerator 1 over denominator tan space x end fraction$

Akan ditunjukkan bahwa

$fraction numerator 1 plus space cotan space x over denominator 1 space minus space cotan space x space end fraction equals fraction numerator 1 plus tan space x over denominator tan space x space minus 1 end fraction$

Perhatikan perhitungan berikut

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 1 plus space cotan space x over denominator 1 space minus space cotan space x space end fraction end cell equals cell fraction numerator 1 plus begin display style fraction numerator 1 over denominator tan space x end fraction end style over denominator 1 minus begin display style fraction numerator 1 over denominator tan x end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator tan space x space plus 1 over denominator tan space x end fraction end style over denominator begin display style fraction numerator tan space x minus 1 over denominator tan x end fraction end style end fraction end cell row blank equals cell up diagonal strike fraction numerator tan space x space plus 1 over denominator tan space x end fraction end strike times fraction numerator up diagonal strike tan space x end strike over denominator tan space x minus 1 end fraction end cell row blank equals cell fraction numerator tan space x space plus 1 over denominator tan space x minus 1 end fraction end cell row blank equals cell fraction numerator 1 plus tan space x over denominator tan space x minus 1 end fraction end cell end table$

Dengan demikian terbukti bahwa $fraction numerator 1 plus space cotan space x over denominator 1 space minus space cotan space x space end fraction equals fraction numerator 1 plus tan space x over denominator tan space x space minus 1 end fraction$ .