Question

Найдите наименьшее значение выражения :
y = cos ( п/5-2x ) + cos ( 7п /15 +2x ) +3

Answer 1

y`=2sin(π/5-2x)-2sin(7π/15+2x)=0
2* 2sin(-2π/15 -2x)cosπ/3=0
-2six(2π/15+2x)=0
six(2π/15+2x)=0
2π/15+2x=πn
2x=-2π/15+πn
x=-π/15+πn/2
y(-π/15)=cos(π/15+2π/15)+cos(7π/15-2π/15)+3=π/5 +cosπ/3+3≈0,848+0,5+3≈4,348