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