4( x - 16 ) - ( 8 - x ) = 10( x + 1 ) - 2 ( 15 + 8x )
4x - 64 - 8 + x = 10x + 10 - 30 - 16x
5x - 72 = - 6x - 20
5x + 6x = - 20 + 72
11x = 52
x = 52/11
x = 4 8/11
Введём дополнительный угол.
Посчитаем C = √(a² + b²)
C = √(1² + 1²) = √2.
Разделим на √2:
sin5x·√2/2 + cos5x·√2/2 = √2/2
sin(π/4) = cos(π/4) = √2/2
cos5x·cos(π/4) + sin5x·sin(π/4) = √2/2
cos(5x - π/4) = √2/2
5x - π/4 = ±π/4 + 2πn, n ∈ Z
5x = ±π/4 + π/4 + 2πn, n ∈ Z
x = ±π/20 + π/20 + 2πn/5, n ∈ Z
Ответ: x = ±π/20 + π/20 + 2πn/5, n ∈ Z.
12= 2*2*3
16=2*2*2*2
НОД=2*2*3*2*2=48
Х не равен 1/2
х не равен -3