Question

докажите что cos 75 + cos 45 - cos 15 = 0

Answer 1

cos 75° + cos 45° - cos15° =cos 75° - cos15° + cos45° =cos (45°+30°) -cos (45°−30°) + cos45 = cos 45°⋅cos 30° − sin 45°⋅sin 30° - cos 45°⋅cos 30° - sin 45°⋅sin 30° + cos45=

= -2 * sin 45°⋅sin 30° + cos45 = -2 * √2/2 * 1/2 + √2/2 = 0