3/х-3 - х+15/(х-3)(х+3) - 2/х
3х(х+3)-х(х+15)-2(х-3)(х+3) / х(х-3)(х+3)
3х²+9х-х²-15х-2(х²-9) / х(х-3)(х+3)
3х²+9х-х²-15х-2х²+18 / х(х-3)(х+3)
0-6х+18 / х(х-3)(х+3)
-6(х-3) / х(х-3)(х+3)
-6 / х(х+3)
Ответ
-6 / х² + 3х
Применим формулу синуса половинного угла слева и синуса двойного угла справа:
2sin²(x/2) = 2·2sin(x/2)cos(x/2)·sin(x/2)
2sin²(x/2) = 4sin²<span>(x/2)cos(x/2)
</span>2sin²(x/2) - 4sin²<span>(x/2)cos(x/2) = 0
</span>2sin²(x/2) ·(1 - 2<span>cos(x/2)) = 0
</span>sin²(x/2) = 0 или 1 - 2<span>cos(x/2) = 0
</span>x/2 = πn, n∈Z cos(x/2) = 1/2
x = 2πn, n∈Z x/2 = π/3 + 2πk, k∈Z или x/2 = - π/3 + 2πm, m∈Z
x = 2π/3 + 4πk, k∈Z x = - 2π/3 + 4πm, m∈Z<span>
</span> 2sin²(x/2) - 4sin²(x/2)cos(x/2) = 0
2sin²(x/2) - 2·2sin²<span>(x/2)cos(x/2) = 0
</span> _______ _______ это выносим
2sin²(x/2) · ( 1 - 2<span>cos(x/2)) = 0</span>
Y=2cosx+3
E(cosx)=[-1;1]
E(2cosx)=[-2;2]
E(2cosx+3)=[-2+3;2+3]=[1;5]