2.sin60+tg 45 - 2.cos 30= 2. V3/2 + 1 - 2. V3/2 = 1
<span>(x²-5x+14)²-30</span><span>(x²-5x+6)</span>-40=0
<span>x²-5x+14=a
a²-30(a-8)-40=0
a²-30a+200=0
a1+a2=30 U a1*a2=200
a1=10⇒</span>x²-5x+14=10⇒<span>x²-5x+4=0⇒x1+x2=5 U x1*x2=4⇒x1=1 U x2=4
a2=20</span>⇒x²-5x+14=20⇒<span>x²-5x-6=0⇒x3+x4=5 U x3*x4=-6⇒x3=-1 U x2=6
x={-1;1;4;6}
</span>
Из формул
sin3a=3cos²asina-sin³a и cos3a=cos³a-3cosasin²a⇒
sin³2a=3cos²2asin2a-sin6a и cos³2a=3cos2asin²2a+cos6a
<span>
sin³2acos6a+cos³2asin6a=(</span>3cos²2asin2a-sin6a)cos6a+(3cos2asin²2a+cos6a)sin6a=
=3cos²2asin2acos6a-sin6acos6a+3cos2asin²2asin6a+cos6asin6a=
=3cos²2asin2acos6a+3cos2asin²2asin6a=3cos2asin2a(cos2acos6a+sin2asin6a)=
=3cos2asin2acos(6a-2a)=3cos2asin2acos4a=3*1/2sin4acos4a=3/2*1/2sin8a=3/4sin8a
Арифметическая прогрессия
d= 16
n = 8
an = a8 = a1 + 7d = x +7·16 = x + 112
x+112 = 390
x = 390 - 112 = 278 ( в первом ряду мест)
S = ( 278 + 390) ·8 : 2 = 668 ·4 = 2672 ( всего мест)