Question

calcule: cos 15° + cos 75°

Answer 1

Calculando cosseno de 15°:
cos(45° - 30°) = cos45° * cos30° + sen45° * sen30°
cos (15°) = √2/2 * √3/2 + √2/2 * 1/2
cos (15°) = √6/4 + √2/4
cos (15°) = (√6+√2)/4

Calculando cosseno de 75°:
cos(45° + 30°) = cos45° * cos30° - sen45° * sen30°
cos(75°) = √2/2 * √3/2 - √2/2 * 1/2
cos(75°) = √6/4 - √2/4
cos(75°) = (√6-√2)/4

cos 15° + cos 75°
(√6+√2)/4 + (√6-√2)/4
(√6+√6+√2-√2)/4
2√6/4
√6/2