Question

(1-tan^2(x))/(1+tan^2x))=cos(2x) помогите доказать это тождество

Answer 1

$\frac{1 - \frac{\sin^2 {x}}{\cos^2{x}}}{1+ \frac{\sin^2 {x}}{\cos^2{x}}} =\cos {2x} \\ \\ \frac{\cos^2 {x} -\sin^2{x}}{\cos^2x + \sin^2{x}}=\cos 2x \\ \\ \frac{\cos2x}{1}=\cos2x \\ \\ \cos2x =\cos 2x$

Answer 2

$\dfrac{1- \frac{sin^2x}{cos^2x} }{1+ \frac{sin^2x}{cos^2x} }=cos2x \\ \\ \dfrac{\frac{cos^2x-sin^2x}{cos^2x} }{\frac{cos^2x+sin^2x}{cos^2x} }=cos2x \\ \\ \frac{cos^2x-sin^2x}{cos^2x} *{\frac{cos^2x}{cos^2x+sin^2x} }=cos2x \\ \\ cos^2x-sin^2x=cos2x \\ cos2x=cos2x$