Question

a) 3^sin^2(x) + 3^cos^2(x) = 4;
б) Найти все корни уравнения, принадлежащие промежутку [-2π;-π/2].


20б.

Answer 1

Или отбор неравенством :
1) -2π≤πk≤-π/2
-2≤k≤-0,5
k=-2,-1
x=-2π,-π
2)-2π≤π/2+2πk≤-π/2
-2π-π/2≤2πk≤-π/2-π/2
-5π/2≤2πk≤-π
-1,25≤k≤-0,5
k=-1
x=-3π/2
3)-2π≤-π/2+2πk≤-π/2
-2π+π/2≤2πk≤-π/2+π/2
-3π/2≤2πk≤0
-3/4≤k≤0
k=0
x=-π/2