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