cos2x+5cosx+3=0 ....note that cos2x = 2cos^x - 1 ....so we have.......
2cos^x - 1 + 5 cosx + 3 = 0 simplify
2cos^x + 5cosx + 2 = 0 factor
(2cosx + 1) (cosx + 2) = 0 setting each factor to 0, we have......
2cosx + 1 = 0 and cosx + 2 = 0
subtract 1 from each side subtract 2 from each side
2cosx = -1 cos x = -2
divide both sides by 2 this has no solution
cosx = -1/2
And the solution to this is x = (2/3)pi + 2pi * n and x = (4/3)pi + 2pi * n .... where n is any integer
Here's a graph......https://www.desmos.com/calculator/wb2x5nbzfv
cos2x+5cosx+3=0 ....note that cos2x = 2cos^x - 1 ....so we have.......
2cos^x - 1 + 5 cosx + 3 = 0 simplify
2cos^x + 5cosx + 2 = 0 factor
(2cosx + 1) (cosx + 2) = 0 setting each factor to 0, we have......
2cosx + 1 = 0 and cosx + 2 = 0
subtract 1 from each side subtract 2 from each side
2cosx = -1 cos x = -2
divide both sides by 2 this has no solution
cosx = -1/2
And the solution to this is x = (2/3)pi + 2pi * n and x = (4/3)pi + 2pi * n .... where n is any integer
Here's a graph......https://www.desmos.com/calculator/wb2x5nbzfv