Задача 31327 [block](2cosx+sqrt(2))/(2sinx+sqrt(2)) =...

bilikto555

2018-11-27 14:24:32

[block](2cosx+sqrt(2))/(2sinx+sqrt(2)) = 0[/block]

[block](sin4x)/(cos4x-1) = 0[/block]

sova

2018-11-27 15:06:47

★

5.
{2cosx+sqrt(2)=0
{2sinx+sqrt(2) ≠ 0

{cosx=-sqrt(2)/2;
{sinx ≠ -sqrt(2)/2

О т в е т. х=(3π/4)+2πn, n ∈ Z

6.
{sin4x=0
{cos4x-1 ≠ 0

{sin4x=0
{cos4x ≠ 1

{4x=πk, k ∈ Z
{4x ≠ 2πn, n ∈ Z

{x=(π/4)*k, k ∈ Z
{x ≠ (π/2)*n, n ∈ Z

(π/4)*k ≠ (π/2)*n
k/4≠n/2
k≠2n
О т в е т. ± (π/4)+πm, m ∈ Z
см. рис.