Question

найдите значение выражения 7sin^2a, если tg^2a=6

Answer 1

$1+tg^2 alpha = frac{1}{cos^2 alpha } \ cos^2 alpha = frac{1}{1+tg^2 alpha} = frac{1}{1+6} = frac{1}{7} \ \ sin^2 alpha =1-cos^2 alpha =1- frac{1}{7} = frac{6}{7} \ \ = textgreater 7sin^2 alpha = 7* frac{6}{7} =6$