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18.03.2013

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cos(cosx) = 1.

___________________________

:

cosx = ±arccos1 + 2πn = 2πn (nZ).

n |2πn| ≤ 1 , n = 0, n, .

cosx = 0,

x = ±π/2 + 2πk, kZ

: x = ±π/2 + 2πk.


cos2x - 3sinx = 2.

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(cos2a = 1 - 2sin2a) :

1 - 2sin2x - 3sinx = 2.

, sinx = y. :

2y2 + 3y + 1 = 0.

: y1 = -1, y2 = -1/2.

sinx = -1 sinx = -1/2.

- x = -π/2 + 2πn, - x = (-1)m(-π/6) + πm (m, nZ).

: x = -π/2 + 2πn x = (-1)m(-π/6) + πm.


2tgx - 3ctgx = 1.

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ctgx = 1/tgx x ≠ πn/2 (nZ)

2tgx - 3/tgx = 1 2tg2x - tgx - 3 = 0.

tgx = y 2y2 - y - 3 = 0 y.

y1 = 3/2, y2 = -1.

:

tgx = 3/2, x = arctg(3/2) + πn, nZ.

tgx = -1, x = arctg(-1) + πm = -π/4 + πm, mZ.

: x = arctg(3/2) + πn x = -π/4 + πm.


3cosx - sin2x = 1 - sin3x.

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3(cosx + sinx) = 1 + sin2x.

cosx + sinx = t 3t = t2. t1 = 0, t2 = 3.

, cosx + sinx = 0, cosx ≠ 0, tgx = -1, x = -π/4 + πn (nZ).

t2 cosx + sinx = 3. , .. cosx, cosx 1, 2.

: x = -π/4 + πn.


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