Pertanyaan

cos 2 2 x cos 4 x = ....

$cos^{2} 2 x cos 4 x = ....$

$\frac{1}{4} (2 cos 4 x + cos 8 x - 1)$
$\frac{1}{4} (2 cos 4 x - cos 8 x + 1)$
$\frac{1}{4} (2 cos 4 x + cos 8 x + 1)$
$\frac{1}{2} (2 cos 4 x - cos 8 x + 1)$
$\frac{1}{2} (2 cos 4 x + cos 8 x + 1)$

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Habis dalam

Klaim

S. Solehuzain

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Ingat rumus perkalian trigonometri 2 cos α cos β = cos ( α + β ) + cos ( α − β ) . Sehingga diperoleh cos 2 2 x cos 4 x = = = = = = = = = = = = = cos 2 x cos 2 x cos 4 x cos 2 x ⋅ 2 1 ( 2 cos 2 x cos 4 x ) 2 1 cos 2 x ( cos ( 2 x + 4 x ) + cos ( 2 x − 4 x ) ) 2 1 cos 2 x ( cos 6 x + cos ( − 2 x ) ) ingat cos ( − α ) = cos α 2 1 cos 2 x ( cos 6 x + cos 2 x ) 2 1 cos 2 x . cos 6 x + 2 1 cos 2 x . cos 2 x 4 1 ( 2 cos 2 x . cos 6 x ) + 4 1 ( 2 cos 2 x . cos 2 x ) 4 1 ( cos ( 2 x + 6 x ) + sin ( 2 x − 6 x ) ) + 4 1 ( cos ( 2 x + 2 x ) + cos ( 2 x − 2 x ) ) 4 1 ( cos 8 x + cos ( − 4 x ) ) + 4 1 ( cos 4 x + cos 0 ) 4 1 ( cos 8 x + cos 4 x ) + 4 1 ( cos 4 x + 1 ) 4 1 cos 8 x + 4 1 cos 4 x + 4 1 cos 4 x + 4 1 4 1 cos 8 x + 2 1 cos 4 x + 4 1 4 1 ( 2 cos 4 x + cos 8 x + 1 ) oleh karena itu, jawaban yang benar adalah C.

Ingat rumus perkalian trigonometri $2 cos α cos β = cos (α + β) + cos (α - β)$ .

Sehingga diperoleh

$cos^{2} 2 x cos 4 x = = = = = = = = = = = = = cos 2 x cos 2 x cos 4 x cos 2 x \cdot \frac{1}{2} (2 cos 2 x cos 4 x) \frac{1}{2} cos 2 x (cos (2 x + 4 x) + cos (2 x - 4 x)) \frac{1}{2} cos 2 x (cos 6 x + cos (- 2 x)) ingat cos (- α) = cos α \frac{1}{2} cos 2 x (cos 6 x + cos 2 x) \frac{1}{2} cos 2 x . cos 6 x + \frac{1}{2} cos 2 x . cos 2 x \frac{1}{4} (2 cos 2 x . cos 6 x) + \frac{1}{4} (2 cos 2 x . cos 2 x) \frac{1}{4} (cos (2 x + 6 x) + sin (2 x - 6 x)) + \frac{1}{4} (cos (2 x + 2 x) + cos (2 x - 2 x)) \frac{1}{4} (cos 8 x + cos (- 4 x)) + \frac{1}{4} (cos 4 x + cos 0) \frac{1}{4} (cos 8 x + cos 4 x) + \frac{1}{4} (cos 4 x + 1) \frac{1}{4} cos 8 x + \frac{1}{4} cos 4 x + \frac{1}{4} cos 4 x + \frac{1}{4} \frac{1}{4} cos 8 x + \frac{1}{2} cos 4 x + \frac{1}{4} \frac{1}{4} (2 cos 4 x + cos 8 x + 1)$