Question

$1)2sin^2-cosx-1=0$
$2)tgx-2ctgx+1=0$
$3)3cos^26x+8sin3xcos3x-4=0$

Answer 1

1) 
2-2cos^2x-cosx-1=0
1-2cos^2x-cosx=0
2cos^2x+cosx-1=0  cosx=t   
2t^2+t-1=0
t1=-1  t2=1/2
x1=П+2Пk
x2=+-П/3+2Пk
2)
tgx=t
t-2/t+1=0   t^2+t-2=0
t1=1     x=П/4+Пk
t2=-2   x=-arctg2+пk

3) 3-3sin^2(6x)-4+4sin6x=0
sin6x=t
4t-3t^2-1=0
3t^2-4t+1=0
t1=1 sin6x=1   6x=П/2+2Пk    x=п/12+Пk/3
t2=1/3  sin6x=1/3 6x=(-1)^karcsin(1/3)+Пk
                               x=1/6*(-1)^k*arcsin(1/3)+Пk/6