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Bentuk cos x − tan x − sec x sec x + tan x ekuivalen dengan ...

Bentuk $\frac{sec x + tan x}{cos x - tan x - sec x}$ ekuivalen dengan ...

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Habis dalam

Klaim

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

jawaban yang tepat adalah D.

Pembahasan

Ingat rumus berikut! Perhatikan perhitungan berikut! Oleh karena itu, jawaban yang tepat adalah D.

Ingat rumus berikut!

$begin mathsize 14px style cosec invisible function application space x equals fraction numerator 1 over denominator sin invisible function application space x end fraction sec invisible function application space x equals fraction numerator 1 over denominator cos invisible function application space x end fraction tan invisible function application space x equals fraction numerator sin invisible function application space x over denominator cos invisible function application space x end fraction sin squared invisible function application space x plus cos squared invisible function application space x equals 1 end style$

Perhatikan perhitungan berikut!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sec invisible function application x plus tan invisible function application x over denominator cos invisible function application x minus tan invisible function application x minus sec invisible function application x end fraction end cell equals cell fraction numerator fraction numerator 1 over denominator cos invisible function application x end fraction plus fraction numerator sin invisible function application x over denominator cos invisible function application x end fraction over denominator cos invisible function application x minus fraction numerator sin invisible function application x over denominator cos invisible function application x end fraction minus fraction numerator 1 over denominator cos invisible function application x end fraction end fraction end cell row blank equals cell fraction numerator fraction numerator 1 plus sin invisible function application x over denominator cos invisible function application x end fraction over denominator fraction numerator cos squared invisible function application x minus sin invisible function application x minus 1 over denominator cos invisible function application x end fraction end fraction end cell row blank equals cell fraction numerator 1 plus sin invisible function application x over denominator cos squared invisible function application x minus sin invisible function application x minus 1 end fraction end cell row blank equals cell fraction numerator 1 plus sin invisible function application x over denominator cos squared invisible function application x minus sin invisible function application x minus open parentheses sin squared invisible function application x plus cos squared invisible function application x close parentheses end fraction end cell row blank equals cell fraction numerator 1 plus sin invisible function application x over denominator cos squared invisible function application x minus sin invisible function application x minus sin squared invisible function application x minus cos squared invisible function application x end fraction end cell row blank equals cell fraction numerator 1 plus sin invisible function application x over denominator negative sin invisible function application x minus sin squared invisible function application x end fraction end cell row blank equals cell fraction numerator 1 plus sin invisible function application x over denominator negative sin invisible function application x open parentheses 1 plus sin invisible function application x close parentheses end fraction end cell row blank equals cell negative fraction numerator 1 over denominator sin invisible function application x end fraction end cell row blank equals cell negative cosec invisible function application x end cell end table end style$

Oleh karena itu, jawaban yang tepat adalah D.