Question

(62,19) тригонометрия

Answer 1

62.
$tg435 + tg375 = \frac{sin(435 + 375)}{cos435 \times cos375} = \frac{sin810}{cos435 \times cos375} = \frac{sin(720 + 90)}{cos75\times cos15} = \frac{1}{ \frac{1}{2} (cos(75 + 15) + cos(75 - 15))} = \frac{2}{cos90 + cos60} = \frac{2}{0 + \frac{1}{2} } = 2 \times 2 = 4$
19)
$\frac{tg72 - ctg48}{1 + tg72 \times ctg48} = \frac{tg72 - ctg(90 - 42)}{1 + tg72 \times ctg(90 - 42)} = \frac{tg72 - tg42}{1 + tg72 \times tg42} = tg(72 - 42) = tg30 = \frac{ \sqrt{3} }{3}$