SOLUTION: using cos3x= 4cos^3x -3cosx find the general solution for cos3x+2cosx=0 Soln: cos3x+2cosx=0 ............(1) or, 4cos^x-3cosx+2cosx=0 {put the given value of cos3x=

Question 823330: using cos3x= 4cos^3x -3cosx
find the general solution for cos3x+2cosx=0
Soln:
cos3x+2cosx=0 ............(1)
or, 4cos^x-3cosx+2cosx=0 {put the given value of cos3x=4cos^x-3cosx in the
above equation (1)}
or, 4cos^3x-cosx=0
or, cosx(4cos^2x-1)=0
now we get, cosx=0 and 4cos^2x-1=0
solve these two equations separately to get the solution.
taking cosx=0
or, cosx=cos90 ,we know the value of cos 90 is zero so put cos90 for 0
or, x=90 degree
now, taking 4cos^2x-1=0
or, cos^2x=1/4
or, cosx=+1/2 and cosx=-1/2
or, cosx=cos60 and cosx=cos120
or, x=60 degree and x=120 degree
hence, the results are x= 90,60,120 degrees.
Found 2 solutions by lwsshak3, deepakpradhan:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
using cos3x= 4cos^3x -3cosx
find the general solution for
cos3x+2cosx=0
interval:[0,2π]

..

..

..
cos(x)=0
x=π/2,3π/2
..
4cos^2(x)-1=0
cos^2(x)=1/4
cosx=�√(1/4)=�1/2
x=π/3,2π/3,4π/3,5π/3
Answer by deepakpradhan(1) (Show Source): You can put this solution on YOUR website!
using cos3x= 4cos^3x -3cosx
find the general solution for cos3x+2cosx=0
Soln:
cos3x+2cosx=0 ............(1)
or, 4cos^x-3cosx+2cosx=0 {put the given value of cos3x=4cos^x-3cosx in the
above equation (1)}
or, 4cos^3x-cosx=0
or, cosx(4cos^2x-1)=0
now we get, cosx=0 and 4cos^2x-1=0
solve these two equations separately to get the solution.
taking cosx=0
or, cosx=cos90 ,we know the value of cos 90 is zero so put cos90 for 0
or, x=90 degree
now, taking 4cos^2x-1=0
or, cos^2x=1/4
or, cosx=+1/2 and cosx=-1/2
or, cosx=cos60 and cosx=cos120
or, x=60 degree and x=120 degree
hence, the results are x= 90,60,120 degrees.
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