\newcommand{\tg}{\mathop{\mathrm{tg}}}{\cos 2v=\cos^2 v-\sin^2 v=\frac{\cos^2 v-\sin^2 v}{\sin^2 v+\cos^2 v}=\frac{{\cos^2 v-\sin^2 v \over \cos^2 v}}{{\sin^2 v+\cos^2 v\over\cos^2 v}}=\frac{1-\tg^2 v}{1+\tg^2 v}}=\frac{1-{49 \over 9}}{1+{49\over 9}}=\frac{-{40\over 9}}{{58\over 9}}=-{20\over 29}