Y⁻² *(2y)⁻¹=0
(1/y²)*(1/2y)=0
1/(2y³)=0. ОДЗ: у≠0
ответ: корней нет.
1. 3x=π/2+πn, n∈Z
x=π/6+πn/3, n∈Z
2. x/2=-π/4+πn, n∈Z
x=-π/2+2πn, n∈Z
3. -4x=π/4+πn, n∈Z
x=-π/16+πn/4, n∈Z
4. 3x-π/6=π/6+πn, n∈Z
3x=π/3+πn, n∈Z
x=π/9+πn/3, n∈Z
5. π/6-2x=π-π/6+πn
-2x=2π/3+πn
x=-π/3+πn/2, n∈Z
1. (1+cos2x)/2 -cos2x =sinx ; x∈[π ;2π] .
(1-cos2x)/2 =sinx ;
sin²x -sinx ;
sinx(sinx -1) =0 ;
[ sinx =0 ; sinx =1 . [ x =πk , x=π/2 +2πk , k∈Z.
учитывая x∈ [π ;2π]
ответ : { π/2 ; π ; 2π }
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2.
5cos²x -9sinx =9 ; cos x<0 .
5(1 - sin²x) - 9sinx = 9 ;
5sin²x +9sinx +4 =0 ;
sinx = (-9 -1)/2*5 = -1. ⇒cosx =0 не решение (по условию cosx <0).
sinx = (-9 +1)/2*5 = - 4/5 .
{ sinx = - 4/5 ; cosx < 0 . * * * π < x <3π/2 * * *
x =arcsin(4/5) + (2k+1)π , k ∈Z .
Решение
<span>Ctg a= - 7/24 , 450<a<540
ctg</span>²<span>a + 1 = 1/sin</span>²a
<span>sin</span>²a = 1 / (ctg²a + 1)
<span>sin</span>²a = 1 / [(-7/24)² + 1] = 1 / [(49/576) + 1] = 576 / 625
sina = 24/25
<span>cosx = - </span>√(1 - sin²a) = - √(1 - 576/625) = - √49/625 = - 7/25
<span>sin</span>²(a/2) = (1 - cosa)/2 = (1 + 7/25)/2 = 32/(25*2) = 16/25
<span>sin(a/2) = 4/5
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