445 а) 4cos²x +4sinx -1= 0;
4(1 - sin²x) +4sinx -1 =0 ;
4sin²x -4sinx -3 =0 ;
sinx = 3/2 _нет решения ;
sinx = -1/2 ;
x= (-1)^(n+1)π/6 +π*k ,k∈Z.
б) 4sin²x - 4cosx -1 = 0 ;
4(1-cos²x ) - 4cosx -1 = 0 ;
4 -4cos²x - 4cosx -1 = 0 ;
4cos²x +4cosx -3 = 0 ;
cosx = -3/2_нет решения ;
cosx = 1/ 2 ;
446. а) tq²x =3tqx ;
tqx(tqx -3) =0 ;
tqx =0 ⇒x =π*k ,k∈Z;
tqx=3⇒x =arctq3 +π*k ,k∈Z.
б) ctqx =ctq²x ;
ctqx(ctq x-1) =0 ;
ctqx =0⇒x =π/2+π*k ,k∈Z ;
ctqx =1 ⇒x =π/4+π*k ,k∈Z.
447. а) √(1+cosx) =sinx ;
sinx ≥ -0 .
1+cosx =sin²x ;
cosx (cosx +1) =0 ;
cosx =0⇒x =π/2+2π*k ,k∈Z ;
cosx = -1⇒x =π+2π*k , k∈Z.
б) √(1-cosx) =sinx ;
sinx ≥ -0 .
1-cosx =sin²x ;
cosx(cosx -1) =0 ;
cosx =0⇒x=π/2+2π*k ,k∈Z ;
cosx =1⇒x= 2π*k , k∈Z.
448. а) sin2x +tqx =0;
2tq x/(1+tq²x) +tqx =0 ;
tqx(tq²x +3) =0 ;
tqx =0 ;
x=π*k , k∈Z.
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2sinxcosx+sinx/cosx =0 ;
sinx(2cos²x +1) = 0 ;
sinx = 0⇒x=π*k , k∈Z.
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б) sinx +ctq²x/2 =0 ;
2sinx/2cosx/2 +cosxx/2)/sinx/2 =0;
cosx/2*( 1+2sin²x/2) =0 ;
cosx/2 =0⇒x/2 =π/2+π*k ,k∈Z.⇔x =π+2π*k ,k∈Z.