can some one please show me how to show that this equation is true?

cot^2x-cos^2x= cot^2x * cos^2x

and i have one more question:

in solving:

4cos^2x-3=0

i get +- sqrt. 3/2

this means that there are 4 answers, but in the book, it gives me 2 :

pi/6+npi and 5pi/6+npi

why?

thanks