решите тригонометрические уравнения:

1) 3sin^2 x-5sinx-8=0
2) 10sin^2 x+17cosx-16=0
3) sin^2 x+8sinx cosx+12cos^2 x=0
4) 4tgx-9ctg+9=0
5) 14sin^2 x-4cos^2 x=5sin 2x
6) 1-5sin 2x-cos 2x= 12cos^2 x

1)sinx=a3a^2-5a-8=0D=25+96=121=11^2a1=(5+11)/6=16/6=2 2/3a2=(5-11)/6=-6/6sinx=2 2/3 нет корнейsinx=-1x=-п/2+2пк2)10(1-cos^2)+17cosx-16=010-10cos^2x+17cosx-16=010cos^2x-17cosx+6=0cosx=a10a^2-17cosx+6=0D=289-240=49=7^2a1=(17+7)/20=24/20a2=(17-7)/20=1/2cosx=24/20 нет корнейcosx=1/2x=+-п/3+2пк3)sin^2x+8sinxcosx+12cos^2x=0 ÷ cos^2xtg^2+8tgx+12=0tgx=aa^2+8a+12=0D=64-48=16=4^2a1=(-8+4)/2=-2a2=(-8-4)/2=-6tgx=-2x=-arctg2+пкtgx=-6x=-arctg6+пк4)4tgx-9×1/tgx+9=04tg^2x+9tgx-9=0tgx=a4a^2+9a-9=0D=81+144=235=15^2a1=(-9+15)/8=-3/4a2=(-9-15)/8=-3tgx=-3/4x=-arctg3/4+пкtgx=-3x=-arctg3+пк5)14sin^2x-4cos^2x-10sinxcosx=0÷cos^2x14tg^2x-10tgx-4=0 tgx=a 14a^2-10a-4=0D=100+224=324=18^2a1=(10+18)/28=1a2=(10-18)/28=-5/14tgx=1x=п/4+пкtgx=-5/14x=-arctg5/14+пк6)1-5sin2x-cos2x-12cos^2x=0cos^2+sin^2x-10sinxcosx-cosx^2+sinx^2-12cos^2x=02sin^2x-10sinxcosx-12cos^2x=0÷cos^2x2tg^2x-10tgx-12=0tgx=a2a^2-10a-12=0D=100+96=196=14^2a1=(10+14)/4=6a2(10-14)/4=-1tgx=6x=arctg6+пкtgx=-1x=-п/4+пк