А) 2 sin²x + 5 cos x - 5 = 0 2-2cos²x+ 5 cos x - 5 = 0 2cos²x-5cosx+3=0 cosx=a 2a²-5a+3=0 D=25-24=1 a1=(5-1)/4=1⇒cosx=1⇒x=2πn a2=(5+1)/4=1,5∉[-1;1] б) cos 2x · cos 3x = sin 6x · sin x 1/2(cosx+cos5x)=1/2(cos5x-cos8x) cosx+cos5x-cos5x+cos8x=0 cosx+cos8x=0 2cos9x/2*cos7x/2=0 cos9x/2=0⇒9x/2=π/2+πn⇒x=π/9+2πn/9 cos7/2=0⇒7x/2=π/2+πn⇒x=π/7+2πn/7
2-2cos²x+ 5 cos x - 5 = 0
2cos²x-5cosx+3=0
cosx=a
2a²-5a+3=0
D=25-24=1
a1=(5-1)/4=1⇒cosx=1⇒x=2πn
a2=(5+1)/4=1,5∉[-1;1]
б) cos 2x · cos 3x = sin 6x · sin x
1/2(cosx+cos5x)=1/2(cos5x-cos8x)
cosx+cos5x-cos5x+cos8x=0
cosx+cos8x=0
2cos9x/2*cos7x/2=0
cos9x/2=0⇒9x/2=π/2+πn⇒x=π/9+2πn/9
cos7/2=0⇒7x/2=π/2+πn⇒x=π/7+2πn/7