1)7sin2y=2siny 2)(3cosx+8sinx)^2=12+55sin^2x

1) 7*sin2y = 2siny 7*(2siny*cosy) - 2siny = 0 7*siny*cosy - siny = 0 siny*(7cosy - 1 ) = 0 siny = 0 ==> y = pik, k ∈z cosy = 1/7 ==> y = ± arсcos(1/7) + 2pik,  k ∈z 2) (3cosx + 8sinx)^2 = 12 + 55sin^2x 9cos^2x + 48sinxcosx + 64sin^2x - 12(sin^2x + cos^2x)  - 55sin^2x = 0 9cos^2x + 48sinxcosx + 64sin^2x - 12sin^2x - 12cos^2x  - 55sin^2x = 0 - 3 sin^2x + 48sinxcosx  - 3 cos^2x = 0   (sin^2x + cos^2x) - 16sinxcosx  = 0   1 – 8sin2x= 0  sin2x = 1/8  2x = arcsin(1/8) + 2pik x = 1/2 * arcsin(1/8) + pik ,  k ∈z x = pi/2 - 1/2* arcsin(1/8) + pik ,  k ∈z

8b^2+10ab-3a^2=(4b-a)(2b+3a)

64b^3-a^3=(4b-a)(16b^2+4ab+a^2)

(4b-a)(2b+3a)/(4b-a)(16b^2+4ab+a^2)=(2b+3a)/(16b^2+4ab+a^2)

1)зх-2 > 0, 3x> 2 ,x> 2/3

2) 2(7-5x)> 0, 14-10x> 0, 10x< 14, x< 7/5

3)1/2(x^2-2)> 0,x^2-2> 0, x> корень из 2, либо   x< -корень из 2

4)7(4-x^2)> 0,4-x^2> 0, x^2< 4, -2< x< 2.