Show that 2sin(x) =(4cos(x)-1)/tan(x) can be written as: 6cos^2(x)-cos(x)-2=0

Rearranging gives:4cos(x)-1 = 2sin(x)tan(x) Substituting in tan(x)=sin(x)/cos(x) gives:4cos(x)-1 = 2sin(x)(sin(x)/cos(x))2sin²(x)=4cos²(x)-4cos(x)Substituting in 2sin²(x) = 2-2cos²(x) (from the trigonometric identity: sin²(x) = 1-cos²(x))2-2cos²(x)=4cos²(x)-4cos(x)Rearranging this by collecting like terms gives:6cos²(x)-cos(x)-2=0