Question

ЛЕГКОЕ ЗАДАНИЕ,

Вычислите 7tg2a+24ctg2a, если sina = 3/5, 0

Answer 1

=31

Пошаговое объяснение:

1.

${sin}^{2} \alpha + {cos}^{2} \alpha = 1 \\( \frac{3}{5})^{2} + {cos}^{2} \alpha = 1 \\ {cos}^{2} \alpha = \frac{16}{25} \\ cos \alpha = \frac{4}{5}$

2.

$sin2 \alpha = 2 \times sin \alpha \times cos \alpha \\ sin2 \alpha = 2 \times \frac{3}{5} \times \frac{4}{5} = \frac{24}{25}$

3.

$cos2 \alpha = {cos}^{2} \alpha - {sin}^{2} \alpha \\ cos2 \alpha = \frac{16}{25} - \frac{9}{25} = \frac{7}{25}$

$tg2 \alpha = \frac{sin2 \alpha }{cos2 \alpha }$

$tg2 \alpha = \frac{24}{25} \div \frac{7}{25} = \frac{24}{7}$

$ctg2 \alpha = \frac{1}{tg2 \alpha} \\ ctg2 \alpha = 1 \div \frac{24}{7} = \frac{7}{24}$

4.

$7 \times tg2 \alpha + 24 \times ctg2 \alpha = 7 \times \frac{24}{7} + 24 \times \frac{7}{24} = \\ 24 + 7 = 31$