4sin^2x+9cosx-6=0

6sin^2+5sinx-11=0

1) 4-4cos²x+9cosx-6=0

4cos²x-9cosx+2=0

cosx=a

4a²-9a+2=0

D=81-32=49

a1 = (9-7) / 8=1/4⇒cosx=1/4⇒x=+-arccos1/4+2πn, n∈Z

a2 = (9+7) / 8=2⇒cosx=2>1 нет решения

2) sinx=a

6a²+5a-1=0

D=25+24=49

a1 = (-5-7) / 12=-1⇒sinx=-1⇒x=-π/2+2πn, n∈Z

a2 = (-5+7) / 12=1/6⇒sinx=1/6⇒x = (-1) ^k*arcsin1/6+πk, k∈Z