Pertanyaan

Jika tan x = t 1 , maka nilai 2 cos 2 x − 1 adalah …

Jika $tan x = \frac{1}{t}$ , maka nilai $2 cos^{2} x - 1$ adalah $\dots$

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

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Klaim

R. Septa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

, maka sisi depan = 1 satuan dan sisi samping = t satuan Sehingga, didapat, Maka, Jadi, jawaban yang tepat adalah C.

, maka sisi depan = 1 satuan dan sisi samping = t satuan

Sehingga,

didapat,

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

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 cos squared x minus 1 end cell equals cell 2 open parentheses fraction numerator t over denominator square root of 1 plus t squared end root end fraction close parentheses squared minus 1 end cell row blank equals cell 2 open parentheses fraction numerator t squared over denominator 1 plus t squared end fraction close parentheses minus 1 end cell row blank equals cell fraction numerator 2 t squared over denominator 1 plus t squared end fraction minus fraction numerator 1 plus t squared over denominator 1 plus t squared end fraction end cell row blank equals cell fraction numerator t squared minus 1 over denominator 1 plus t squared end fraction end cell row blank equals cell fraction numerator t squared minus 1 over denominator t squared plus 1 end fraction end cell end table end style$

Jadi, jawaban yang tepat adalah C.