Tg7⁰*tg83⁰+tg19⁰*tg71⁰=

$tg7^{o}\cdot tg83^{o}= \frac{cos(83^{o}-7^{o})-cos(83^{o}+7^{o})}{cos(83^{o}-7^{o})+cos(83^{o}+7^{o})} = \frac{cos76^{o}-cos 90^{o}}{cos76^{o}+cos90^{o}} = \frac{cos76^{o}-0}{cos76^{o}+0} =1$

$tg19^{o}\cdot tg71^{o}= \frac{cos(71^{o}-19^{o})-cos(71^{o}+19^{o})}{cos(71^{o}-19^{o})+cos(71^{o}+19^{o})} = \frac{cos52^{o}-cos 90^{o}}{cos52^{o}+cos90^{o}} = \frac{cos52^{o}-0}{cos52^{o}+0} =1$

Ответ. 1+1=2