3cosx - √3sinx = 0 /:cosx ≠ 0
3 - √3tgx = 0
- √3tgx = - 3
√3tgx = 3
tgx = 3/√3
tgx = √3
x = pi/3 + pik, k ∈ Z
<span>sin3x*cos2x=sin5x
</span><span>sin3x*cos2x=sin(3x+2x)
</span>sin3x*cos2x=sin3x cos2x+sin2x cos3x
sin2x cos3x=0
1) sin2x=0 2x=πn, n∈Z x=(π/2)n, n∈Z
2) cos3x=0 3x=π/2+πn, x=π/6+πn/3 , n∈Z
X²+5x-14>0
x1+x2=-5 U x1*x2=-14
x1=-7 U x2=2
+ _ +
-------------(-7)------------(2)--------------
x∈(-∞;-7) U (2;∞)
Log0,5(1-x)>-1
ОДЗ: 1-x>0 y=log0,5(x)-убывающая
x<1
log0,5(1-x)>-log0,5(0,5)
log0,5(1-x)>log0,5(2)
1-x<2
x>1-2
x>-1
Даём ответ с учётом ОДЗ:
x∈(-1;1)
S5=y1(d^5-1)/(d-1)=2(243-1)/2=242