Sin3x -sin5x = 0 ;
-2sinx *cos4x = 0 ;
[ sinx =0; cos4x =0. [ x =π*k ; 4x =π/2 +π*k , k∈Z. [ x =π*k ; x =π/8 +π/4*k , k∈Z.
ответ :: π*k ; π/8 +π/4*k , k∈Z .
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2sin2x +5sinx =0;
2*2sinx*cosx +5sinx =0 ;
4sinx(cosx +5/4) = 0 ;
[sinx =0 ; cosx +5/4 =0 . [sinx =0 ; cosx = -5/4 < -1 (не имеет решения) .
sinx =0 ;
x =π*k ,k∈Z.
ответ : π*k ,k∈Z.
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sin2x +cos²x =0;
2sinx*cosx +cos²x =0;
2cosx(sinx +1/2cos x) =0 ; * * * [ cosx =0 ;sinx +1/2cosx =0. * * *
a) cosx =0 ;
x =π/2 +π*k ; k∈Z.
b) sinx +1/2cos x =0;
sinx = -1/2cos x *** cosx ≠0 ***
tqx =-1/2 ;
x = -arctq(1/2) +π*k k∈Z .
ответ : arctq(1/2) +π*k , k∈Z .
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8cos²x - 10sinx -11 = 0 ;
8(1 - sin²x) -10sinx -11 = 0 ;
8sin²x +10sinx +3 =0 ; замена : t=sinx.
8t² +10t +3 =0 ;
D/4 =5² -8*3 =1² .
t₁ = (- 5 -1)/8 = - 3/4 ;
t ₂= (- 5 +1)/8 =- -1/2.
sinx₁= -3/4;
x₁= (-1)^(n+1)arcsin(3/4) +π*k ,k∈Z ;
sinx₂= -1/2 ;
.x₂ = (-1)^π/6 +π*k ,k∈Z .
ответ : (-1)^(n+1)arcsin(3/4) +π*k , (-1)^(n+1)*π/6 +π*k , k∈ Z ;
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