дробь3/2*tgX*sin2X-2cos^2 X=8sinX-5

помогите решить!

3/2 tg x*sin 2x-2cos^2 x=8sin x-5

cos x не равно 0

3/2 tg x*2sin xcosx-2cos^2 x=8sin x-5

3 sin^2 x-2cos^2 x=8sin x-5

3 sin^2 x-2+2sin^2 x=8sin x-5

5 sin^2 x-8sin x+3=0

5 sin^2 x-5sin x-3 sin x+3=0

(5sin x-3) (sin x-1) = 0

5sin x=3 т. к. sin x не равно 1 по ОДЗ

sin x=3/5

x = (-1) ^n arcsin (3/5) + πn