10cos^2x+11cosx-6=0

3cos^2x-11sinx-9=0

7tgx-2ctgx+5=0

1) cosx=a

10a²+11a-6=0

D=121+240=361 √D=19

a1 = (-11-19) / 20=-30/20=-1,5∈[-1; 1]-нет решения

a2 = (-11+19) / 20=8/20=0,4⇒cosx=0,4⇒x = + - arccos0,4+2πn

2) 3 (1-2sin²x) - 11sinx-9=0

6sin²x+11sinx+6=0

a=sinx

6a²+11a+6=0

D=121-144=-23-решения нет

3) 7tgx-2/tgx+5=0

7tg²x+5tgx-2=0

a=tgx

7a²+5a-2=0

D=25+56=81 √D=9

a1 = (-5-9) / 14=-1⇒tgx=-1⇒x=-π/4+ππn

a2 = (-5+9) / 14=4/14=2/7⇒tgx=2/7⇒x=arstg2/7+πn