general solution4cos2x-6cosx+5=0

Question

Determine the general solution for the above equation

Answer 1

4cos(2x)-6cos(x)+5=4(2cos²(x)-1)-6cos(x)+5=0,

8cos²(x)-4-6cos(x)+5=0,

8cos²(x)-6cos(x)+1=0=(2cos(x)-1)(4cos(x)-1).

So cos(x)=½ or ¼. x=π/3+2nπ, 1.3181+2nπ; also 2nπ-π/3, 2nπ-1.3181 (radians), where n is an integer.

In degrees this is: x=60°+360n°, 75.52°+360n°, 360n°-60°, 360n°-75.52°. 

Decimals are approximate.