1)sinx=a
3a^2-5a-8=0
D=25+96=121=11^2
a1=(5+11)/6=16/6=2 2/3
a2=(5-11)/6=-6/6
sinx=2 2/3 нет корней
sinx=-1
x=-п/2+2пк
2)10(1-cos^2)+17cosx-16=0
10-10cos^2x+17cosx-16=0
10cos^2x-17cosx+6=0
cosx=a
10a^2-17cosx+6=0
D=289-240=49=7^2
a1=(17+7)/20=24/20
a2=(17-7)/20=1/2
cosx=24/20 нет корней
cosx=1/2
x=+-п/3+2пк
3)sin^2x+8sinxcosx+12cos^2x=0 ÷ cos^2x
tg^2+8tgx+12=0
tgx=a
a^2+8a+12=0
D=64-48=16=4^2
a1=(-8+4)/2=-2
a2=(-8-4)/2=-6
tgx=-2
x=-arctg2+пк
tgx=-6
x=-arctg6+пк
4)4tgx-9×1/tgx+9=0
4tg^2x+9tgx-9=0
tgx=a
4a^2+9a-9=0
D=81+144=235=15^2
a1=(-9+15)/8=-3/4
a2=(-9-15)/8=-3
tgx=-3/4
x=-arctg3/4+пк
tgx=-3
x=-arctg3+пк
5)14sin^2x-4cos^2x-10sinxcosx=0÷cos^2x
14tg^2x-10tgx-4=0 tgx=a 14a^2-10a-4=0
D=100+224=324=18^2
a1=(10+18)/28=1
a2=(10-18)/28=-5/14
tgx=1
x=п/4+пк
tgx=-5/14
x=-arctg5/14+пк
6)1-5sin2x-cos2x-12cos^2x=0
cos^2+sin^2x-10sinxcosx-cosx^2+sinx^2-12cos^2x=02sin^2x-10sinxcosx-12cos^2x=0÷cos^2x
2tg^2x-10tgx-12=0
tgx=a
2a^2-10a-12=0
D=100+96=196=14^2
a1=(10+14)/4=6
a2(10-14)/4=-1
tgx=6
x=arctg6+пк
tgx=-1
x=-п/4+пк