cos 45° + cos 165° + cos 285°
Matematika
Megaprnm
Pertanyaan
cos 45° + cos 165° + cos 285°
1 Jawaban
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1. Jawaban Anonyme
Trigonometry.
cos (180° - θ°) = -cos θ°
cos (360°- θ°) = cos θ°
cos A - cos B = -2 sin 1/2 (A + B) 1/2 (A - B)
cos 45° + cos 165° + cos 285°
= cos 45° + (-cos 15°) + cos 75°
= 1/2 √2 + cos 75° - cos 15°
= 1/2 √2 -2 sin 1/2 (75° + 15°) sin 1/2 (75° - 15°)
= 1/2 √2 - 2 sin 45° sin 30°
= 1/2 √2 - 2 (1/2 √2) (1/2)
= 0