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(a b) =a 2ab+b
(a b) =a 3a b+3ab b
a -b =(a+b)(a-b)
a b =(a b)(a ab+b ),
. .
xn-an=(x-a)(xn-1+axn-2+a xn-3+...+an-1)
ax +bx+c=a(x-x1)(x-x2)
x1
ax +bx+c=0
:
ap ag = ap+g
ap:ag=a p-g
(ap)g=a pg
ap /bp = (a/b)p
ap bp = abp
a0=1; a1=a
a-p = 1/a
p a =b => bp=a
p ap b = p ab
a ; a = 0
____
/ __ _
p g a = pg a
___ __
pk agk = p ag
p ____
/ a p a
/ =
b p b
a 1/p = p a
p ag = ap/g

ax +bx+c=0; (a 0)
x1,2= (-b D)/2a; D=b -4ac
D>0 x1 x2 ;D=0 x1=x2
D<0, .
:
x1+x2 = -b/a
x1 x2 = c/a
. :
x + px+q =0
x1+x2 = -p
x1 x2 = q
p=2k (p-.)
x +2kx+q=0, x1,2 = -k (k -q)
:
loga x = b => ab = x; a>0,a 0
a loga x = x, logaa =1; loga 1 = 0
loga x = b; x=ab
loga b = 1/(log b a)
logaxy = logax + loga y
loga x/y = loga x loga y
loga xk =k loga x (x >0)
logak x =1/k loga x
loga x = (logc x)/( logca); c>0,c 1


an = an-1 +d
2an= an-1 + an+1
an = a1 + d(n-1)
Sn = n(a1 + an )/2
Sn = (a1+d(n-1))n/2
Sn= a1 + a2 +...+an

bn = bn-1 q
b2n = bn-1 bn+1
bn = b1 qn-1
Sn= (bnq- b1)/(q-1)
Sn = b1 (qn-1)/(q-1)
S= b1/(1-q)
.
sin x = a/c
cos x = b/c
tg x = a/b=sinx/cos x
ctg x = b/a = cos x/sin x
sin (p -a ) = sin a
sin (p /2 -a ) = cos a
cos (p /2 -a ) = sin a
cos (a + 2p k) = cos a
sin (a + 2p k) = sin a
tg (a + p k) = tg a
ctg (a + p k) = ctg a
sin a + cos a =1
tg a = cosa / sina , a p n, n Z
tga ctga = 1, a (p n)/2, n Z
1+tg a = 1/cos a , a p (2n+1)/2
1+ ctg a =1/sin a , a p n
:
sin(x+y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y cos x sin y
cos (x+y) = cos x cos y sin x sin y
cos (x-y) = cos x cos y + sin x sin y
tg(x+y) = (tg x + tg y)/ (1-tg x tg y )
x, y, x + y p /2 + p n
tg(x-y) = (tg x tg y)/ (1+tg x tg y)
x, y, x y p /2 + p n
.
sin 2a = 2sin a cos a
cos 2a = cos a sin a = 2 cos a 1 =
= 1-2 sin a
tg 2a = (2 tga )/ (1-tg a )
1+ cos a = 2 cos a /2
1-cosa = 2 sin a /2
tga = (2 tg (a /2))/(1-tg (a /2))
- .
sin a /2 = (1 cos a )/2
cos a /2 = (1 + cosa )/2
tg a /2 = sina /(1 + cosa ) = (1-cos a )/sin a
a p + 2p n, n Z
- .
sin x + sin y = 2 sin ((x+y)/2) cos ((x-y)/2)
sin x sin y = 2 cos ((x+y)/2) sin ((x-y)/2)
cos x + cos y = 2cos (x+y)/2 cos (x-y)/2
cos x cos y = -2sin (x+y)/2 sin (x-y)/2
sin (x+y)
tg x + tg y =
cos x cos y
sin (x y)
tg x tgy =
cos x cos y
. .
sin x sin y = (cos (x-y) cos (x+y))
cos x cos y = (cos (x-y)+ cos (x+y))
sin x cos y = (sin (x-y)+ sin (x+y))
. -
2 tg x/2
sin x =
1+ tg x/2
1-tg 2/x
cos x =
1+ tg x/2

sin x = m ; |m| = 1
x = (-1)n arcsin m + p k, k Z
sin x =1 sin x = 0
x = p /2 + 2p k x = p k
sin x = -1
x = -p /2 + 2 p k
cos x = m; |m| = 1
x = arccos m + 2p k
cos x = 1 cos x = 0
x = 2p k x = p /2+p k
cos x = -1
x = p + 2p k
tg x = m
x = arctg m + p k
ctg x = m
x = arcctg m +p k
sin x/2 = 2t/(1+t2); t tg
cos x/2 = (1-t )/(1+t )

a + b + g =180

a = b +c 2bc cos a
b = a +c 2ac cos b
c = a + b 2ab cos g
. .
. .
.
.
.
:
p= (a+b+c)
_____________
S = p(p-a)(p-b)(p-c)
S = ab sin a
S.=(a 3)/4
S = bh/2
S=abc/4R
S=pr
.

S = (a+b)/2 h

S= p R
S=(p R a )/360


V=S

V=abc

V =1/3S. H
S.= S.+ S.
:
H . _____
V = 3 (S1+S2+ S1S2)
S1 S2 .
S.=S.+S1+S2

V=1/3 p R H
S. =p Rl
S.= p R(R+1)

S.= p l(R1+R2)
V=1/3p H(R12+R1R2+R22)

V=S. H
: S.=P. H
S.=S+2S.
:
S.=P a
V = S a, -. .
P
S . .
.
V=p R H ; S.= 2p RH
S.=2p R(H+R)
S.= 2p RH
.
V = 4/3 p R
S = 4p R

V = 2/3 p R H
H .

V=p H (R-H/3)
S=2p RH