Question

calcule o valor da seguinte soma: S= cos 15 + cos 75 + sen 15 + sen 75

Answer 1

S = Cos (45°-30°) + cos (45°+30°) + sen (45°- 30°) + sen (45° + 30°)
S = (cos 45° x cos 30° + sen45° x sen 30°) + (cos 45° x cos 30° - sen 45° x sen 30° ) + (sen 45° x Cos 30° - sen 30° x cos 45°) + (sen 45° x Cos 30° + sen 30° x cos 45°)
S = (√2/2 x √3/2 + √2/2 x 1/2) + (√2/2 x √3/2 - √2/2 x 1/2) + (√2/2 x √3/2 - 1/2 x √2/2) + (√2/2 x √3/2 + 1/2 x √2/2)
S = (√6/4 + √2/4) + (√6/4 - √2/4) + (√6/4 - √2/2) + √6/4 + √2/4)
S = √6