Решите уравнения:

[tex]3sin^2 x - 5sin x cos x +2cos^2 x=0[/tex]

 

[tex]cos^4 13x - sin^4 13x=cos7x[/tex]

1) Делим на cos^2 (x), обозначим tgx = t:

3t^2 - 5t + 2 = 0      D = 1    t1 = (5+1)/6 = 1,  t2 = (5-1)/6 = 2/3

Или:  tgx = 1               x = П/4  + Пк

         tgx = 2/3           x = arctg(2/3) + Пn,     k,n прин. Z.

 2) (cos^2(13x) - sin^2(13x))*(cos^2(13x) + sin^2(13x)) = cos7x

                       |                                      |

                   cos(26x)                               1

cos26x  -  cos7x = 0

-2sin(19x/2) * sin(33x/2) = 0

sin(19x/2) = 0                              sin(33x/2) = 0

19x/2 = Пk                                   33x/2 = Пn,

x = 2Пk/19                                   x = 2Пn/33

Ответ: 2Пk/19;  2Пn/33;  k,n прин. Z.