F(1/x)=(1/x-1) :(3-1/x)=(1-x)/x :(3x-1)x=(1-x)/x*x/((3x-1)=(1-x)/(3x-1)
Sin5x *cos<span>²2x =1 ;
</span>sin5x *(1+cos2*2x) /2 = <span>1 ;
</span>sin5x +sin5x*cos4x =2 ;
sin5x +( sin(5x +4x) +sin(5x-4x) ) / 2 = 2 ;
2sin5x +sin9x +sinx = 4 ⇔ { sinx =1 ; sin5x = 1; sin9x =1.⇔
{ x =π/2 +2πk ; 5x = π/2 +2πm ; 9x =π/2 +2πn ,k,m,n ∈ Z. ⇒
<span>x =π/2 +2πk ; </span>x = (π/2 +2πm)/5 ; x =(π/2 +2πn)/9 ,k,m,n ∈ Z.<span>
⇔</span>x =π/2 +2πk , k <span>∈ Z.
</span>* * * (π/2 +2πm)/5=π/2 +2πk ⇔2πm =2π +10πk ⇔m=1+5k<span> * * *</span>
* * * (π/2 +2πn)/9 =π/2 +2πk ⇔2πn = 4π +18πk ⇔<span>n=2+9k * * *
</span>
ответ : π/2 +2πk , k ∈ Z.
* * * * * * *
cos² α/2 =(1+cos2<span>α)/2 ;
</span>sinα*cosβ =( sin(α+β) + sin(α-β) ) /2.
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|2sin5x +sin9x+sinx | ≤|2sin5x| +|sin9x|+|sinx| ≤ <span>2*1+1+1 = 4</span>