Question

Выражение 1-tg^2 a / 1+tg^2 a можно преобразовать к

Answer 1

$\frac{1-tg^2 \, \alpha }{1+tg^2 \, \alpha }}=\frac{1 - \frac{\sin^2{ \alpha }}{\cos^2{ \alpha }} }{\frac{1}{\cos^2{ \alpha }}}=\cos^2{ \alpha } \cdot (1 - \frac{\sin^2{ \alpha }}{\cos^2{ \alpha }})= \\\\ =\cos^2{ \alpha } - \sin^2{ \alpha }=\cos{2 \alpha }$

Answer 2

$\frac{1-tg^{2}a}{1+tg^{2}a} =(1- \frac{sin^{2}a}{cos^{2}a} ):(1+ \frac{sin^{2}a}{cos^{2}a} )=\frac{cos^{2}a-sin^{2}a}{cos^{2}a} :\frac{sin^{2}a+cos^{2}a}{cos^{2}a} = \\ \frac{cos^{2}a-sin^{2}a}{cos^{2}a} * \frac{cos^{2}a}{sin^{2}a+cos^{2}a} =\frac{cos^{2}a-sin^{2}a}{1} * \frac{1}{1} =cos2a \\$