2cos2x -4cosx =1
2(2cos²x -1) -4cosx -1=0; *** cosx= t **
4cos²x -4cosx -3 =0;
1) cosx =3/2 > 1
cosx = -1/2 ;
x =(+/-)2π/3 +2π*k ; k∈Z.
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2) 8sin²x +sinxcosx+cos²x =4;
8sin²x +sinxcosx+cos²x =4cos²x +4sin²x ;
4sin²x +sinxcosx -3cos²x =0; (cosx ≠0
4tq²x +tqx -3 =0;
tqx = -1 ⇒x = - π /4 +π*k ,k ∈Z .
tqx= 3/4⇒x= arctq(3/4) +π*k , k∈Z .
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3) 4cos²x(1-cos2x) =1+cos2x ;
4cos²x(1-cos2x) =2cos²x ;
2cos²x(1 -cos2x) -cos²x =0 ;
2cos²x(1 -cos2x -1/2)=0 ;
cosx =0 ⇒ x =π/2 +π*k , , k∈Z.
cos2x = 1/2 ;
2x = (+/-)π/3 +2π*k;
x= (+/-) π/6 +π*k , k∈Z.