Question

Вычислить: 4cos840°-√48*sin600°+ctg²30° =

Answer 1

4cos840°-√48*sin600°+ctg²30° =4*cos(840-2*360) - √48*sin(600-360) + (√3)^2= 4*cos(120) -√48 * sin 240 + 3 = 4* (-cos 60) -√48 * sin (180 + 60) +3 = -4*0,5 + √48*(√3/2) + 3 = -2 + (√144/2) + 3 = -2 + 12/2 + 3 = -2 + 6 + 3 = 7

Ответ: 7.

Answer 2

4cos840° = 4cos(840-720)° = 4cos120° = -2

√48*sin600° = √48*sin(600-360)° = √48*sin240° = -4√3

ctg²30° = (1/tan30°)² = (1/√3)² = 1/3

Итого: -2 - 4√3 + 1/3 = (-6 - 12√3)/3 = -2 - 4√3, ответ: -2 - 4√3.