1) 6sin^2(x)+15sin(3¶/2+x)-12=0, [-5¶; - 7¶/2]

2) 2cos(x-11¶/2)*cosx=sinx, [-5¶; - 4¶]

3) cosx=(cos(x/2)-sin(x/2))^2 - 1

16sin²x-15cosx-12=06-6cos²x-15cosx-12=0cosx=a6a²+15a+6=02a²+5a+2=0D=25-16=9a1=(-5-3)/4=-2⇒cosx=-2<-1 нет решенияa2=(-5+3)/4=-1/2⇒cosx=-1/2x1=-2π/3+2πn,n∈z U x2=2π/3+2πk,k∈z-5π≤-2π/3+2πn≤-7π/2-30≤-4+12n≤-21-26≤12n≤-17-13/6≤n≤-17/12n=-2⇒x=-2π/3-4π=-14π/3-5π≤2π/3+2πk≤-7π/2-30≤4+12k≤-21-34≤12k≤-25-17/6≤k≤-25/12нет решенияОтвет х=-14π/322sinx*cosx=sinx2sinxcosx-sinx=0sinx*(2cosx-1)=0sinx=0⇒x1=πn,n∈z-5π≤πn≤-4π-5≤n≤-4n=-5⇒x=-5πn=-4⇒x=-4πcosx=1/2⇒x2=-π/3 +2πk,k∈z U x3=π/3+2πt,t∈z-5π≤-π/3+2πk≤-4π-15≤-1+6k≤-12-14≤6k≤-11-7/3≤k≤-11/6k=-2⇒x=-π/3-4π=-13π/3-5π≤π/3+2πt≤-4π-15≤1+6t≤-12-16≤6t≤-13-8/3≤t≤-13/6нет решенияОтвет x={-5π;-4π;-13π/3}3cosx=cos²x/2-2cosx/2*sinx/2+sin²x/2-1cosx=1-sinx-1cosx=-sinxcosx+sinx=0/cosx1+tgx=0tgx=-1⇒x=-π/4+πn