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18.03.2013

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sin5x cos3x = sin9x cos7x.

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:

1/2(sin8x + sin2x) = 1/2(sin16x + sin2x);

sin8x = sin16x;

sin16x - sin8x = 0, :

2cos12x sin4x = 0.

cos12x = 0 sin4x = 0.

cos12x = 0, 12x = π/2 + πn, x = (1 + 2n)π/24 (nZ).

sin4x = 0, 4x = πm, x = πm/4 (mZ).

: x = (1 + 2n)π/24 x = πm/4.


cos2x + cos4x + cos6x = 0.

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(cos2x + cos6x) + cos4x = 0;

2cos4xcos2x + cos4x = 0;

cos4x(2cos2x + 1) = 0.

:

cos4x = 0, 4x = π/2 + πn, x = π/8 + πn/4 (nZ).

2cos2x + 1 = 0 cos2x = -1/2, 2x = ±2π/3 + 2πm, x = ±π/3 + πm (mZ).

: x = π/8 + πn/4 x = ±π/3 + πm.


cos5x = cos2x.

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:

-2sin(7x/2)sin(3x/2) = 0;

sin(7x/2)sin(3x/2) = 0;

sin(7x/2) = 0, sin(3x/2) = 0.

: 7x/2 = πn x = 2πn/7 (nZ).

: 3x/2 = πn x = 2πm/3 (mZ).

: x = 2πn/7 x = 2πm/3.


sin3x - 2cos2xsinx = 0.

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, sinx :

sinx(sin2x - 2cos2x) = 0.

:

sinx = 0, x = πn (nZ).

sin2x - 2cos2x = 0. , . cos2x ≠ 0 :

tg2x - 2 = 0;

tg2x = 2;

tgx = ±2;

x = ±arctg2 + πm.

: x = πn x = ±arctg2 + πm.


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