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??????:

? ????????? ??????? ??????? ????????? ????? ????? ?????????

?? ?????????, ?????????????? ????????????? ? ???, ????? ?

?????? ????? ????????? ????? 0. ????? ??????? ???????? ? ??-

???????? ?????? ?????????? ?????????. ????? ??? ????? ?????

?????????? ????????????? ??? ????? ?????????, ????????? ???-

????????? ??????? ?????????????.

??????. sin 2x - cos x = 0.

2 sin x cos x - cos x = 0 cos x(2 sin x - 1) = 0.

x

=

2

+

n,

x

=

(-1)k

?

6

+ k,

n, k

Z.

??????. sin 4x = sin 6x.

sin

4x

-

sin

6x

=

0

2

sin(

4x-6x 2

)

cos(

4x+6x 2

)

=

0

-2 sin x cos 5x = 0 sin x = 0 ? cos 5x = 0.

?????:

x

=

n, n

Z

?

x

=

10

+

1 5

?

k.

??????. cos 3x = sin 5x.

? cxo=s?3?x1?6?-?+, cso4inns,((n24x--5Zx4)?) ==x

00=?4 s+-in2(4ski,-nk(3xx)-=Z22 +.05x. )

sin(

3x+

2

2

-5x

)

=

0.

??????. sin 2x + sin 8x = 2 cos 3x.

sin + sin ??????????? ?????????, ????????? ??????? ???

:

2 sin 5x ? cos 3x = 2 cos 3x cos 3x ? (2 sin 5x - 2) = 0.

?????, cos 3x = 0 ? sin 5x =

2 2

.

x

=

6

+

1 3

? n, n

Z

?

x

=

(-1)k? 20

+

1 5

?

k, k

Z.

??????. sin2 2x + sin2 3x + sin2 4x + sin2 5x = 2.

1 2

(1

-

cos

4x)

+

1 2

(1

-

cos

6x)

+

1 2

(1

-

cos

8x)

+

1 2

(1

-

cos

10x)

=

2,

cos 4x + cos 10x + cos 6x + cos 8x = 0,

2 cos 7x cos 3x + cos 7x + cos x = 0,

2 cos 7x(cos 3x + cos x) = 0 4 cos 7x cos 2x cos x = 0.

????? cos 7x = 0, cos 2x = 0, cos x = 0.

?????:

x

=

14

+

n 7

,

x

=

4

+

k 2

,

x

=

2

+ m,

n, k, m

Z.

??????. 2 sin2 x + sin 2x = sin x + cos x.

2 sin2 x + 2 sin x cos x - (sin x + cos x) = 0,

(sin x

+

cos x)(2 sin x

-

1)

=

0

tg

x

=

-1

?

sin

x

=

1 2

.

?????:

x

=

-

4

+

n,

x

=

(-1)k

?

6

+ k,

n, k

Z.

?????????? ??? ???? ?????? ?????: ???????????? ?????????

???? a cos + b sin .

1

??????. cos 3x - sin x = 3(cos x - sin 3x).

? ? csion?s?(?3?6?x??+?:+?x3, xs=)i3n-(s8xin+s-i3nx(2n132=,)+x=six=n)0x=1?2+0c+os(32kc2x,oss+ninx,(4k2)x2-=s6Zi0)n..c(o6s+(4x32+x2))==si0n.(

3

+

x);

2

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