Question

(62,19) тригонометрия

Answer 1

62.
$tg435 + tg375 = frac{sin(435 + 375)}{cos435 times cos375} = frac{sin810}{cos435 times cos375} = frac{sin(720 + 90)}{cos75times cos15} = frac{1}{ frac{1}{2} (cos(75 + 15) + cos(75 - 15))} = frac{2}{cos90 + cos60} = frac{2}{0 + frac{1}{2} } = 2 times 2 = 4$
19)
$frac{tg72 - ctg48}{1 + tg72 times ctg48} = frac{tg72 - ctg(90 - 42)}{1 + tg72 times ctg(90 - 42)} = frac{tg72 - tg42}{1 + tg72 times tg42} = tg(72 - 42) = tg30 = frac{ sqrt{3} }{3}$