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h 2- (v ),

h'' + h = 0,
h(0) = 0,
h'(0) = 0.

h = 0. (h .)

1- h' - vvv

h'h'' + h'h = 0

.

[(h')2 + h2]' = 0 = 2(h'h'' + h'h)

. (h')2 + h2 . ( v 0 .) h(0) = 0, h'(0) = 0

[h'(x)]2 + [h(x)]2 = 0 (v - )

h(x)=0 .

31

h 2- (v ),

h'' + h = 0,
h(0) = a,
h'(0) = b

h = b sin + a cos.

g(x) = h(x) - b sin(x) - a cos(x) .

g'(x) = h'(x) - b cos(x) + a sin(x)
g''(x) = h''(x) + b sin(x) + a sin(x)

. Vv h'' + h = 0, h(0) = 0, h'(0) = 0 . v -

0 = g(x) = h(x) - b sin(x) - a cos(x)
h(x) = b sin(x) - a cos(x)

.

31 - v. . ( . v!)

32

x, y v

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)
cos(x+y) = cos(x)cos(y) - sin(x)sin(y).

-

() = sin(x+y)

.

'(x) = cos(x+y)
''(x) = -sin(x+y)

. Vv + '' = 0, (0) = sin(y), '(0) = cos(y) . 31- v -

() = sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

. - . 㺺 . v.

sin2(x) + cos2(x) = 1 32- v . .

x+y=a, x-y=b x = (a + b)/2, y = (a - b)/2

. sin(a)-sin(b), cos(a)-cos(b), cos(a)+cos(b) vv .

. v cos(x)cos(y) - ( cos(x)cos(y) ?)

. tan(x-y), cot(x+y), cot(x-y) . ( v .)

.. - sin(x)cos(y), sin(x)sin(y), cos(x)cos(y) vv .

v v, v . v . ( .)

x=y sin(2a) = 2sin(a)cos(a), cos(2a) = cos2a - sin2a . v . ( .)

sin, cos , 30 , 60 vv . vv vvv , v , .

<-- (2) | vv | (1)-->


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