Question

дробь3/2*tgX*sin2X-2cos^2 X=8sinX-5

помогите решить!

Answer 1

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