Pertanyaan

Jika diketahui tan θ = a maka nilai cos 2 θ = ...

Jika diketahui $tan θ = a$ maka nilai $cos 2 θ = ...$

$begin mathsize 12px style fraction numerator 1 minus a over denominator 1 plus a squared end fraction end style$
$begin mathsize 12px style fraction numerator a squared over denominator 1 plus a squared end fraction end style$
$begin mathsize 12px style fraction numerator 1 minus a over denominator 1 plus a end fraction end style$
$begin mathsize 12px style fraction numerator 1 minus a squared over denominator 1 plus a squared end fraction end style$
$begin mathsize 12px style fraction numerator 1 over denominator 1 plus a squared end fraction end style$

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

maka gambar segitiga siku-sikunya yaitu Diperoleh Untuk sudut rangkap cosinus memenuhi

maka gambar segitiga siku-sikunya yaitu

Diperoleh

$begin mathsize 12px style sin space theta equals fraction numerator a over denominator square root of a squared plus 1 end root end fraction cos space theta equals fraction numerator a over denominator square root of a squared plus 1 end root end fraction end style$

Untuk sudut rangkap cosinus memenuhi

$begin mathsize 12px style cos space 2 theta equals cos squared space theta minus sin squared space theta rightwards double arrow open parentheses fraction numerator 1 over denominator square root of a squared plus 1 end root end fraction close parentheses squared minus open parentheses fraction numerator 1 over denominator square root of a squared plus 1 end root end fraction close parentheses squared rightwards double arrow fraction numerator 1 over denominator a squared plus 1 end fraction minus fraction numerator 1 over denominator a squared plus 1 end fraction rightwards double arrow fraction numerator 1 minus a squared over denominator 1 plus a squared end fraction end style$