find all solutions to the conditional equations in the interval (0,2π)
1. cos2X + cosX = 0
2. tan2X = tanX
3. cos2X - sinX = 0
4. sin2X + cosX = 0
2007-09-08 15:45:37 · 2 answers · asked by cigarette lighter 1 in Science & Mathematics ➔ Mathematics
cos2x= cos^2x-sin^2x = 2cos^2x-1
so2cos^x+cosx-1= 0
cos x= z
2z^2+z -1= 0
z= ((-1+-sqrt(9))/4
z= 1/2 and z= -1
cos x = 1/2 and x = pi/3 and 5pi/3
cos x= -1 and x= pi
2) tan 2x = tanx/(1-tan^2x)
so tan x= tan x/(1-tan^2x)
tanx= 0 x=0 and x=pi
3) the same as 1 using cos^2x=1-sin^2x
4) use sin 2x = 2 sin x cos x
2007-09-08 16:14:38 · answer #1 · answered by santmann2002 7 · 0⤊ 0⤋
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2016-10-10 05:43:44 · answer #2 · answered by ? 4 · 0⤊ 0⤋