Pertanyaan

sec x + tan x sec x − tan x = ....

$\frac{sec x - tan x}{sec x + tan x} = ....$

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S. Indah

Master Teacher

Mahasiswa/Alumni Universitas Lampung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat! Sehingga, Oleh karena itu, jawaban yang benar adalah D.

Ingat!

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x end cell equals cell fraction numerator sin space x over denominator cos space x end fraction end cell row cell s e c space x end cell equals cell fraction numerator 1 over denominator cos space x end fraction end cell row cell sin squared x plus cos squared x end cell equals 1 end table$

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row cell square root of fraction numerator s e c space x minus tan space x over denominator s e c space x plus tan space x end fraction end root end cell equals cell square root of fraction numerator begin display style fraction numerator 1 over denominator cos space x end fraction end style minus begin display style fraction numerator sin space x over denominator cos space x end fraction end style over denominator begin display style fraction numerator 1 over denominator cos space x end fraction end style plus begin display style fraction numerator sin space x over denominator cos space x end fraction end style end fraction end root end cell row blank equals cell square root of fraction numerator begin display style fraction numerator 1 minus sin space x over denominator cos space x end fraction end style over denominator begin display style fraction numerator 1 plus sin space x over denominator cos space x end fraction end style end fraction end root end cell row blank equals cell square root of fraction numerator 1 minus sin space x over denominator 1 plus sin space x end fraction end root cross times square root of fraction numerator 1 minus sin space x over denominator 1 minus sin space x end fraction end root end cell row blank equals cell fraction numerator 1 minus sin space x over denominator square root of 1 minus sin squared x end root end fraction end cell row blank equals cell fraction numerator 1 minus sin space x over denominator square root of 1 minus left parenthesis 1 minus cos squared x right parenthesis end root end fraction end cell row blank equals cell fraction numerator 1 minus sin space x over denominator square root of cos squared x end root end fraction end cell row blank equals cell fraction numerator 1 minus sin space x over denominator cos space x end fraction end cell row blank equals cell fraction numerator 1 over denominator cos space x end fraction minus fraction numerator sin space x over denominator cos space x end fraction end cell row blank equals cell s e c space x minus tan space x end cell end table$

Oleh karena itu, jawaban yang benar adalah D.

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