5tgx-8ctgx+6=0 |*tgx
5tg^2x+6tgx-8=0
tgx=t
5t^2+6t-8=0
D=36-4*5*(-8)=196
t=-2
t=4/5
1)tgx=-2
x=arctg(-2)+pik . k=z
2)tgx=4/5
x=arctg(4/5)+pik . k=z
sin2x+1=4cos^2x
2sinxcosx=4cos^2x-1 | /cos^2x
2tgx=4-1/cos^2x
-2tgx=(1/cos^2x -1) -3
-2tgx=tg^2x-3
tg^2x+2tgx-3=0
t^2+2t-3=0
t=1
t=-3
1)tgx=1
x=pi/4+pik . k=z
2)tgx=-3
x=arctg(-3)+pik . k=z
14cos^2x+3=3cos^2x-10sin^2x
11cos^2x+10sin^2x+3=0
10+cos^2x+3=0
cosx^2=-13 -нет корней
5tgx-8ctgx+6=0 |*tgx
5tg^2x+6tgx-8=0
tgx=t
5t^2+6t-8=0
D=36-4*5*(-8)=196
t=-2
t=4/5
1)tgx=-2
x=arctg(-2)+pik . k=z
2)tgx=4/5
x=arctg(4/5)+pik . k=z
sin2x+1=4cos^2x
2sinxcosx=4cos^2x-1 | /cos^2x
2tgx=4-1/cos^2x
-2tgx=(1/cos^2x -1) -3
-2tgx=tg^2x-3
tg^2x+2tgx-3=0
tgx=t
t^2+2t-3=0
t=1
t=-3
1)tgx=1
x=pi/4+pik . k=z
2)tgx=-3
x=arctg(-3)+pik . k=z
14cos^2x+3=3cos^2x-10sin^2x
11cos^2x+10sin^2x+3=0
10+cos^2x+3=0
cosx^2=-13 -нет корней