8 sin^2x-2cosx-5=0 Пожалуйста помогите, заранее спасибо!
8sin^2x-2cosx-5=0,
8(1-cos^2x)-2cosx-5=0,
-8cos^2x-2cosx+3=0,
8cos^2x+2cosx-3=0,
cosx=t,
8t^2+2t-3=0,
D=100,
t1=-3/4,
t2=1/2,
cosx=-3/4,
x=-+arccos(-3/4) +2pi*k, kєZ,
x=-+(pi-arccos(3/4)) +2pi*k, kєZ,
cosx=1/2,
x=-+arccos(1/2)+2pi*k, kєZ,
x=-+pi/3 + 2pi*k, kєZ
8 sin^2x-2cosx-5=0
8cosx^2+2cosx-3=0
8x2 + 2x - 3 = 0D = b2 - 4acD = 4 + 96 = 100 = 10^2
x1,2 = -b ± √D/2ax1 = -2 + 10/16 = 8/16 = 1/2x2 = -2 - 10/16 = - 12/16 = - 3/4Ответ: x1 = 1/2 ; x2 = - 3/4
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Answers & Comments
8sin^2x-2cosx-5=0,
8(1-cos^2x)-2cosx-5=0,
-8cos^2x-2cosx+3=0,
8cos^2x+2cosx-3=0,
cosx=t,
8t^2+2t-3=0,
D=100,
t1=-3/4,
t2=1/2,
cosx=-3/4,
x=-+arccos(-3/4) +2pi*k, kєZ,
x=-+(pi-arccos(3/4)) +2pi*k, kєZ,
cosx=1/2,
x=-+arccos(1/2)+2pi*k, kєZ,
x=-+pi/3 + 2pi*k, kєZ
Verified answer
8 sin^2x-2cosx-5=0
8cosx^2+2cosx-3=0
8x2 + 2x - 3 = 0
D = b2 - 4ac
D = 4 + 96 = 100 = 10^2
x1,2 = -b ± √D/2a
x1 = -2 + 10/16 = 8/16 = 1/2
x2 = -2 - 10/16 = - 12/16 = - 3/4
Ответ: x1 = 1/2 ; x2 = - 3/4