Jika tan x=p, maka nilai 2 sinx cosx adalah …

Pertanyaan

Jika $\style{font-size:14px}{\tan\;x=p}$ , maka nilai $\style{font-size:14px}{2\;\sin x\;\cos x}$ adalah $\style{font-size:14px}\dots$

$begin mathsize 14px style fraction numerator p over denominator p squared minus 1 end fraction end style$
$begin mathsize 14px style fraction numerator p over denominator p squared plus 1 end fraction end style$
$begin mathsize 14px style fraction numerator 2 p over denominator p squared minus 1 end fraction end style$
$begin mathsize 14px style fraction numerator 2 p over denominator square root of p squared plus 1 end root end fraction end style$

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

, maka sisi depan = p dan sisi samping = 1, sehingga sisi miring = .

Didapat,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell depan over miring equals fraction numerator p over denominator square root of p squared plus 1 end root end fraction end cell row cell cos space x end cell equals cell samping over miring equals fraction numerator 1 over denominator square root of p squared plus 1 end root end fraction end cell row blank blank blank end table end style$

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 times sin space x times cos space x end cell equals cell 2 times fraction numerator p over denominator square root of p squared plus 1 end root end fraction times fraction numerator 1 over denominator square root of p squared plus 1 end root end fraction end cell row blank equals cell fraction numerator 2 p over denominator p squared plus 1 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah D.