Pertanyaan

Buktikan identitas trigonometri berikut. d. sin P + cos P 1 + tan P = sec P

Buktikan identitas trigonometri berikut.

d. $\frac{1 + tan P}{sin P + cos P} = sec P$

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E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator 1 plus tan space P over denominator sin space P plus cos space P end fraction equals sec space P$ .

Pembahasan

Ingat! Akan dibuktikan Perhatikan perhitungan berikut ini Dengan demikian terbukti bahwa .

Ingat!

$tan space P equals fraction numerator sin space P over denominator cos space P end fraction$
$sec space P equals fraction numerator 1 over denominator cos space P end fraction$

Akan dibuktikan

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

Perhatikan perhitungan berikut ini

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

Dengan demikian terbukti bahwa $fraction numerator 1 plus tan space P over denominator sin space P plus cos space P end fraction equals sec space P$ .