1) 7 tg x - 2 ctg x+5=0
7/ctg x -2 ctg x+5=0
(7-2ctg^2 x + 5 ctg x)/ctg x=0
7-2ctg^2 x + 5 ctg x=0
-2ctg^2 x+ 5 ctg x+7=0
2ctg^2 x-5 ctg x-7=0
ctg x = a
2a^2-5a-7=0
D=(-5)^2 -4*2*(-7)= 25+56=81 V(корень)D=9
x1=(5+9)/4=3,5
x2=(5-9)/4=-1
ctg x = 3.5 - решений нет
ctg x = -1
x = -pi /4+pi*n, neZ
2)sin5x+sin7x=0
2sin6x*cos2x = 0
2sin6x = 0 или cos 2x = 0
a) 2sin6x = 0
sin 6x=0
x= (pi*n) / 6, neZ
b) cos 2x = 0
x=pi/4+(pi*n)/2, neZ