10sin²x+5sinxcosx+cos²x=3(sin²x+cos²x)
10sin²x+5sinxcosx+cos²x=3sin²x+3cos²x
Поделим на cos²x
cos²x≠0
cosx≠0
x≠п/2+пn,n€z
10tg²x+5tgx+1=3tg²x+3
7tg²x+5tgx-2=0
tgx=t
7t²+5t-2=0
D=25-4*7*(-2)=81
t1=-5+9/14=4/14=2/7
t2=-5-9/14=-1
tgx=2/7
x=arctg2/7+пn,n€z
tgx=-1
x=-п/4+пn,n€z