СРОЧНОНАЙДИТЕ х : sin(2x) sin(6x) = cos(x)cos(3x)

sin(2x)* sin(6x) = cos(x)*cos(3x) ;

( сos(6x-2x) - cos(6x+2x) ) / 2 = ( cos(3x+x) +cos(3x-x) ) / 2 ;

cos4x -cos8x = cos4x + cos2x;

cos8x +cos2x =0 ;

2cos( (8x+2x)/2)  *cos( (8x-2x)/2)=0 ;

cos5x*cos3x =0 ;

cos5x = 0  5x =/2 +k , k  x =/10 +k/5 ,k

или

cos3x =0 3x =/2 +k , k  x =/6 +k/3 ,k

Sin2xsin6x=cosxcos3x

2*sinxcosx*2sin3xcos3x-cosxcos3x=0
cosxcos3x(4sinxsin3x-1)=0

1)cosx=0;x=/2+n
2)cos3x=0;3x=/2+k;x=/6+k/3

3)4sinxsin3x=1
sinxsin3x=1/4
sinx*(3sinx-4sinx)=1/4
3sinx-4sinx-1/4=0
16sinx-12sinx+1=0
sinx=tgt;0
16t-12t+1=0
D/4=36-16=20
t=(625)/16=(35)/8
t1=(3-5)/8
t2=(3+5)/8
sinx=(3+5)/8
sinx=(3-5)/8=(6-25)/16=
(5)-25+1)/16=(5-1)/16=(5-1)/4
sinx=(5-1)/4
x=(-1)arcsin((5-1)/4)+n


sinx=(5+1)/4
x=(-1)arcsin((5+1)/4)+n