Question

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

Answer 1

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