50 б помогите lim (cos^2x-cos^2(2x))/x^2 x--->0

$\lim_{x \to 0} \frac{cos^2x-cos^22x}{x^2} = \lim_{x \to 0} \frac{cos^2x-cos^4x-sin^4x+2cos^2xsin^2x}{x^2} =\\= \lim_{x \to 0} \frac{cos^2x(1-cos^2x)-sin^4x+2cos^2xsin^2x}{x^2} =\\ = \lim_{x \to 0} \frac{3sin^2xcos^2x-sin^4x}{x^2} = \frac{sin^2x(3cos^2x-1)}{x^2} =\\ = \lim_{x \to 0} \frac{x^2(3cos^2x-1)}{x^2} =\lim_{x \to 0} 3cos^2x-1=3-1=2$

Ответ: 2