Pertanyaan

Nilai dari cos 2 0 ∘ + cos 4 0 ∘ + cos 6 0 ∘ + ... + cos 16 0 ∘ + cos 18 0 ∘ adalah...

Nilai dari $cos 2 0^{\circ} + cos 4 0^{\circ} + cos 6 0^{\circ} + ... + cos 16 0^{\circ} + cos 18 0^{\circ}$ adalah...

$- 1$
$- \frac{1}{2}$
$0$
$\frac{1}{2}$
1

M. Rochmat

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat! Rumus jumlah kosinus: cos x + cos y = 2 cos ( 2 x + y ) cos ( 2 x − y ) Sehingga: = = = = = cos 2 0 ∘ + cos 4 0 ∘ + cos 6 0 ∘ + cos 8 0 ∘ + cos 10 0 ∘ + cos 12 0 ∘ + cos 14 0 ∘ + cos 16 0 ∘ + cos 18 0 ∘ ( cos 16 0 ∘ + cos 2 0 ∘ ) + ( cos 14 0 ∘ + cos 4 0 ∘ ) + ( cos 10 0 ∘ + cos 8 0 ∘ ) + cos 6 0 ∘ + cos 12 0 ∘ + cos 18 0 ∘ 2 cos ( 2 16 0 ∘ + 2 0 ∘ ) cos ( 2 16 0 ∘ − 2 0 ∘ ) + 2 cos ( 2 14 0 ∘ + 4 0 ∘ ) cos ( 2 14 0 ∘ − 4 0 ∘ ) + 2 cos ( 2 10 0 ∘ + 8 0 ∘ ) cos ( 2 10 0 ∘ − 8 0 ∘ ) + cos 6 0 ∘ + cos 12 0 ∘ + cos 18 0 ∘ 2 cos 9 0 ∘ cos 7 0 ∘ + 2 cos 9 0 ∘ cos 5 0 ∘ + 2 cos 9 0 ∘ cos 1 0 ∘ + 2 1 − 2 1 − 1 0 + 0 + 0 + 0 − 1 − 1 Dengan demikian, cos 2 0 ∘ + cos 4 0 ∘ + cos 6 0 ∘ + ... + cos 16 0 ∘ + cos 18 0 ∘ = − 1 . Oleh karena itu, jawaban yang tepat adalah A.

Ingat!

Rumus jumlah kosinus: $cos x + cos y = 2 cos (\frac{x + y}{2}) cos (\frac{x - y}{2})$

Sehingga:

$= = = = = cos 2 0^{\circ} + cos 4 0^{\circ} + cos 6 0^{\circ} + cos 8 0^{\circ} + cos 10 0^{\circ} + cos 12 0^{\circ} + cos 14 0^{\circ} + cos 16 0^{\circ} + cos 18 0^{\circ} (cos 16 0^{\circ} + cos 2 0^{\circ}) + (cos 14 0^{\circ} + cos 4 0^{\circ}) + (cos 10 0^{\circ} + cos 8 0^{\circ}) + cos 6 0^{\circ} + cos 12 0^{\circ} + cos 18 0^{\circ} 2 cos (\frac{16 0 ^{\circ} + 2 0 ^{\circ}}{2}) cos (\frac{16 0 ^{\circ} - 2 0 ^{\circ}}{2}) + 2 cos (\frac{14 0 ^{\circ} + 4 0 ^{\circ}}{2}) cos (\frac{14 0 ^{\circ} - 4 0 ^{\circ}}{2}) + 2 cos (\frac{10 0 ^{\circ} + 8 0 ^{\circ}}{2}) cos (\frac{10 0 ^{\circ} - 8 0 ^{\circ}}{2}) + cos 6 0^{\circ} + cos 12 0^{\circ} + cos 18 0^{\circ} 2 cos 9 0^{\circ} cos 7 0^{\circ} + 2 cos 9 0^{\circ} cos 5 0^{\circ} + 2 cos 9 0^{\circ} cos 1 0^{\circ} + \frac{1}{2} - \frac{1}{2} - 1 0 + 0 + 0 + 0 - 1 - 1$