Pertanyaan

Jika diketahui tan 2 x + 1 = a 2 , maka nilai sin 2 x adalah …

Jika diketahui $tan^{2} x + 1 = a^{2}$ , maka nilai $sin^{2} x$ adalah $\dots$

$begin mathsize 14px style fraction numerator a squared minus sign 1 over denominator a squared end fraction end style$
$begin mathsize 14px style fraction numerator 1 minus sign a squared over denominator a squared end fraction end style$
$begin mathsize 14px style fraction numerator a squared plus 1 over denominator a squared end fraction end style$
$begin mathsize 14px style fraction numerator a squared over denominator a squared minus sign 1 end fraction end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B

Pembahasan

Ingat: 1. . 2. . Maka Jadi, jawaban yang tepat adalah B

Ingat:

1. sin squared x plus cos squared x equals 1 rightwards arrow 1 minus cos squared x equals sin squared x .

2. $tan space x equals fraction numerator sin space x over denominator cos space x end fraction$ .

Maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared x plus 1 end cell equals cell a squared end cell row cell fraction numerator sin squared x over denominator cos squared x end fraction plus 1 end cell equals cell a squared end cell row cell sin squared x plus cos squared x end cell equals cell a squared times cos squared x end cell row 1 equals cell a squared times open parentheses 1 minus sin squared x close parentheses end cell row cell 1 over a squared end cell equals cell 1 minus sin squared x end cell row cell sin squared x end cell equals cell 1 minus 1 over a squared end cell row cell sin squared x end cell equals cell fraction numerator a squared minus 1 over denominator a squared end fraction end cell end table$

Jadi, jawaban yang tepat adalah B