Question

упростите
1/1+ tg ^2 альфа
вся эта дробь + sin ^2 альфа

Answer 1

$frac{1}{1+tg^2 alpha } +sin^2 alpha = frac{1}{1+ frac{sin^2 alpha }{cos^2 alpha } } +sin^2 alpha = frac{cos^2 alpha }{cos^2 alpha +sin^2 alpha } +sin^2 alpha =\=cos^2 alpha +sin^2 alpha =1$

Answer 2

$frac{1}{1+ tg^{2} alpha } + sin^{2} alpha = frac{1}{1+ frac{ sin^{2} alpha }{cos ^{2} alpha } } + cos^{2} alpha$ =$= frac{ cos^{2} alpha }{ cos^{2} alpha + sin^{2} alpha } +sin^{2} alpha = cos^{2} alpha + sin^{2} alpha =1$