Pertanyaan

Diketahui 0 ≤ x < 2 π . Jika 4 sin 2 x + 8 sin 2 x = 7 cos 2 x ,maka nilai dari tan 2 x adalah ....

Diketahui $0 \leq x < \frac{π}{2}$ . Jika $4 sin 2 x + 8 sin^{2} x = 7 cos 2 x$ , maka nilai dari $tan 2 x$ adalah ....

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M. Robo

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Perhatikan bahwa Sehingga Jadi, jawaban yang tepat adalah A.

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 4 sin invisible function application 2 x plus 8 sin squared invisible function application x end cell equals cell 7 cos invisible function application 2 x end cell row cell 4 open parentheses 2 sin invisible function application x cos invisible function application x close parentheses plus 8 sin squared invisible function application x end cell equals cell 7 open parentheses cos squared invisible function application x minus sin squared invisible function application x close parentheses end cell row cell 8 sin invisible function application x cos invisible function application x plus 8 sin squared invisible function application x end cell equals cell 7 open parentheses cos squared invisible function application x minus sin squared invisible function application x close parentheses end cell row cell 8 sin invisible function application x open parentheses cos invisible function application x plus sin invisible function application x close parentheses end cell equals cell 7 open parentheses cos invisible function application x minus sin invisible function application x close parentheses open parentheses cos invisible function application x plus sin invisible function application x close parentheses end cell row cell 8 sin invisible function application x end cell equals cell 7 open parentheses cos invisible function application x minus sin invisible function application x close parentheses end cell row cell 8 sin invisible function application x end cell equals cell 7 cos invisible function application x minus 7 sin invisible function application x end cell row cell 8 sin invisible function application x plus 7 sin invisible function application x end cell equals cell 7 cos invisible function application x end cell row cell 15 sin invisible function application x end cell equals cell 7 cos invisible function application x end cell row cell fraction numerator sin invisible function application x over denominator cos invisible function application x end fraction end cell equals cell 7 over 15 end cell row cell tan invisible function application x end cell equals cell 7 over 15 end cell end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 2 x end cell equals cell fraction numerator 2 tan invisible function application x over denominator 1 minus tan squared invisible function application x end fraction end cell row blank equals cell fraction numerator 2 open parentheses 7 over 15 close parentheses over denominator 1 minus open parentheses 7 over 15 close parentheses squared end fraction end cell row blank equals cell fraction numerator 14 over 15 over denominator 1 minus 49 over 225 end fraction end cell row blank equals cell fraction numerator 14 over 15 over denominator 225 over 225 minus 49 over 225 end fraction end cell row blank equals cell fraction numerator 14 over 15 over denominator 176 over 225 end fraction end cell row blank equals cell 14 over 15 cross times 225 over 176 end cell row blank equals cell 7 over 1 cross times 15 over 88 end cell row blank equals cell 105 over 88 end cell end table end style$

Jadi, jawaban yang tepat adalah A.