1)5sinx-3+5cosx=5(sinx+cosx)-3=5(sinx+sin(π/2-x))-3=5*2sinπ/4 cos(x-π/4)-3=
=5√2cos(x-π/4)-3
2)7sinx-5+7cosx=7√2cos(x-π/4)-5
3)1-sinx ctgx cosx=1-sinx*(cosx/sinx)*cosx=1-cos²x=sin²x
4) (cos²x-sin²x) / (2cos²x-1) = cos2x / cos2x =1
5) (cos2a+1)tg²a-1=2cos²a*(sin²a / cos²a)-1=2sin²a-1= -cos2a
6)(sina+cosa)²-1=sin²a+2sina cosa+cos²a-1=2sina cosa=sin2a
Исходное не пишу
1) 14 4/5+4/15=14 12/15+4/15=14 16/15=15 1/15
2) 2 2/3:4=8/3:4=2/3
3) 15 1/15:22 3/5=226/15:113/5=(226*5)/(15*113)=2/3
4) 2/3+2/3=4/3=1 1/3
1)a7=3a2
a1+6d=3a1+3d
2a1=3d
2)S6=(2a1+5d)*6/2
48=(2a1+5d)*6/2
2a1+5d=16
3d+5d=16
d=2
3)S14=(2a1+13d)*14/2
S14=16d*7=16*2*7=224
Ответ:224
<span>|x^2-5x|-6>0
</span><span>|x^2-5x|>6</span>⇒
<span>[x</span>²-5x<-6 (1)
<span>[x</span>²-5x>6 (2)
<span>1)x</span>²-5x+6<0
<span>D=25-24=1>1
x1+x2=5 U x1*x2=6
x1=2 x2=3
+ _ +
-----------------(2)---------------------(3)------------------
2<x<3
2)x</span>²-5x-6>0
<span>D=25+24=49>0
x1+x2=5 U x1*x2=-6
x1=-1 x2=6
+ _ +
--------------(-1)------------------(6)--------------
x<-1 U x>6
Ответ x</span>∈(-∞;-1) U (2;3) U (6;∞)<span>
</span>