cosx+cos3x+cos5x is an expression which could be simplified. It is not an equation. However, the expression is equated to 0 and the solution for x is given in the following para.
Cosx+cos3x+cos5x=0
Cosx+{cos3x+cos5x}=0
cosx+2cos[(3x+5x)/2]cos[(5x-3x)/2] = 0
cosx+2cos4x*cosx = 0
cosx{1+2cos4x} = 0
cosx=0 or 1+2cos4x = 0
Cosx =0, for x=90 and 270 degrees
1+2cos4x = 0 gives:
cos4x = -1/2.
4x = 120 or 4x = 240 . General solution 4x= (n*360 +or- 120) degree. So,
x = n*90+30 or x=n*90-30 degree.
The angles,30 or 120 or 150 or 210 300 and 330 degrees hold good in 0 to 360 dgrees.(p/6,4p/6, 5p/3,7p/6,10p/6 and 11p/6 radians)
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