Question

Найти значение выражения: 1 - tg^2 15° / 1 + tg^2 15°

Answer 1

$\frac{1-tg^2(15)}{1+tg^2(15)} =(1- \frac{sin^2(15)}{cos^2(15)} ):(1+ \frac{sin^2(15)}{cos^2(15)} )=$
$= \frac{cos^2(15)-sin^2(15)}{cos^2(15)}:\frac{cos^2(15)+sin^2(15)}{cos^2(15)}= \frac{cos^2(15)-sin^2(15)}{cos^2(15)}: \frac{1}{cos^2(15)} =$
$=\frac{cos(30)}{cos^2(15)}* cos^2(15)=cos(30)= \frac{ \sqrt{3} }{2}$