9-5=4 части разница
72:4=18 книг на одну часть
5*18=90 книг на первой
9*18=162 книги на второй
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2.y=tan(12)×2x
y =(-0.63585997)×2x
y=(-1.2717199)x
y=-1.2717199x
Sin 3x + Sin 5x = 2(Cos² 2x - Sin² 3x)<span> </span>
<span>Для левой части ур-ия применим формулу суммы синусов: </span>
Sin x + Sin y = 2Sin ((x + y)/2) · Cos ((x - y)/2)<span> </span>
<span>А для правой части формулы понижения степени: </span>
Cos² x = (1 + Cos 2x) / 2
Sin² x = (1 - Cos 2x) / 2<span> </span>
<span>То есть: </span>
<span>2Sin 4x · Cos x = 2 · ((1 + Cos 4x)/2 - (1 - Cos 6x)/2)) </span>
<span>2Sin 4x · Cos x = 1 + Cos 4x - 1 + Cos 6x </span>
<span>2Sin 4x · Cos x = Cos 4x + Cos 6x </span>
<span>Для правой части ур-ия применим формулу суммы косинусов: </span>
Cos x + Cos y = 2Cos ((x + y)/2) · Cos ((x - y)/2)<span> </span>
<span>2Sin 4x · Cos x = 2Cos 5x * Cos x </span>
<span>2Sin 4x · Cos x - 2Cos 5x * Cos x = 0 </span>
<span>Выносим общий множитель </span>2Cos x<span>: </span>
<span>2Cos x · (Sin 4x - Cos 5x) = 0 </span>
<span>Отсюда: </span>
<span>Cos x = 0 ⇒ </span>x = ±π/2 + 2πk, k — целое<span> </span>
<span>Sin 4x - Cos 5x = 0 </span>
<span>Cos (π/2 - 4x) - Cos (5x) = 0 </span>
<span>Применяем формулу разности косинусов: </span>
Cos x - Cos y = -2Sin ((x + y)/2) · Sin ((x - y)/2)<span> </span>
<span>То есть: </span>
<span>-2Sin ((π/2 + x)/2) · Sin ((π/2 - 9x)/2) = 0 </span>
<span>1) Sin ((π/2 + x)/2) = 0 </span>
<span>(π/2 + x)/2 = πk </span>
<span>π/2 + x = 2πk </span>
<span>x = -π/2 + 2πk </span>
<span>2) Sin ((π/2 - 9x)/2) = 0 </span>
<span>(π/2 - 9x)/2 = πk </span>
<span>π/2 - 9x = 2πk </span>
<span>9x = π/2 - 2πk </span>
<span>x = π/18 - 2π/(9k) </span>
Ответ:
x = ±π/2 + 2πk, k — целое
x = π/18 - 2π/(9k)