Question

Помогите, пожалуйста, 60 баллов!!!

Answer 1

$3 sin ^{2} x - 7sin x cos x + 14 { cos}^{2} x = 2 times 1 \ 3 sin ^{2} x - 7sin x cos x + 14 { cos}^{2} x = 2({ cos}^{2} x + { sin}^{2} x) \ 3 sin ^{2} x - 7sin x cos x + 14 { cos}^{2} x = 2{ cos}^{2} x + 2{sin}^{2} x \ sin ^{2} x - 7sin x cos x + 12 { cos}^{2} x = 0 : : |: cos ^{2} x, : cos x neq 0 \ { tg}^{2} x - 7 tg x + 12 = 0 \ \ tg x = t \ \ {t}^{2} - 7t + 12 = 0 \ t _{1} = 3 \ t _{2} = 4 \ \ 1) tg x = 3 \ x = arctg 3 + pi n, n in Z \ \ 2)tg x = 4 \ x = arctg 4+ pi n, n in Z \ \ OTBET: arctg 3 + pi n ; arctg 4+ pi n, n in Z$

Answer 2

3sin²x-7sinxcosx+14cos²x-2(sin²x+cos²x)=0
sin²x-7sinxcosx+12cos²x=0
:cos²x≠0
tg²x-7tgx+12=0
tgx=t
t²-7t+12=0
D=49-48=1
t=(7±1)/2
t1=4
t2=3
tgx=4;x=arctg4+πk
tgx=3;x=arctg3+πk;k€Z