Question

Помогите, пожалуйста, 60 баллов!!!

Answer 1

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

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