8 sin 15° sin 75° = 8 sin 15° sin (90° - 15°) =
= 8 sin 15° cos 15° = 4 (2 sin 15° cos 15°) =
= 4 sin 30° = 4 · 1/2 = 2
<em>8 sin 15° sin 75° = 2</em>
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Использованы формулы
sin (90° - α) = cos α
sin (2α) = 2 sin α cos α
X-5<8/(x+2) ОДЗ: x+2≠0 x≠-2
x-5-(8/(x+2))<0
(x-5)*(x+2)-8<0
x²-5x+2x-10-8<0
x²-3x-18<0
x²-3x-18=0 D=81
x₁=6 x₂=-3
(x-6)(x+3)<0
-∞____+____-3____-____6____+_____+∞
x∈(-3;6).
Согласно ОДЗ:
x∈(-3;-2)U(-2;6).