From the trigonometric identity:
[tex] cos^{2}x + sin^{2} x[/tex]=1
Making [tex] sin^{2} [/tex]x the subject we get:
[tex] sin^{2} [/tex]x=1-[tex] cos^{2} [/tex]x
On evaluating the left hand side and replacing [tex] sin^{2} [/tex]x with 1-[tex] cos^{2} [/tex]x;
2(1-[tex] cos^{2} [/tex]x)-1
This gives
=2-2[tex] cos^{2}x [/tex]-1
=1-2[tex] cos^{2} [/tex]x
From the identity in [tex]cos^{2} [/tex]x+[tex] sin^{2} [/tex]x=1, replace 1 in the equation to get;
[tex] cos^{2} [/tex]x+[tex] sin^{2} [/tex]x-2[tex] cos^{2} [/tex]x
=[tex] sin^{2} [/tex]2x-[tex] cos^{2} [/tex]x
