Question

тригонометрия 45 баллов​

Answer 1

Ответ:

4.

$2tgx - 6ctgx + 11 = 0 \\ 2tgx - \frac{6}{tgx} + 11 = 0$

замена:

$tgx = t$

t не равно 0.

$2t - \frac{6}{t} + 11 = 0 \\ 2 {t}^{2} + 11t - 6 = 0 \\ d = 121 + 48 = 169 \\ t1 = \frac{ - 11 + 13}{4} = \frac{1}{2} \\ t2 = - \frac{24}{4} = - 6 \\ \\ tgx = \frac{1}{2} \\ x1 = arctg( \frac{1}{2} ) + \pi \: n \\ \\ tgx = - 6 \\ x2 = - arctg(6) + \pi \: n$

5.

$22 \sin ^{2} ( x ) - 9 \sin(2x) = 20 \\ 22 \sin ^{2} ( x ) - 18 \sin(x) \cos(x) - 20( { \sin }^{2} (x) + { \cos}^{2} (x)) = 0 \\ 2 { \sin}^{2} (x) - 18 \sin(x) \cos(x) - 20 { \cos }^{2} (x) = 0 \\ { \sin }^{2} (x) - 9 \sin(x) \cos(x) - 10 { \cos}^{2}(x) = 0$

разделим на cos^2x, не равный 0.

${tg}^{2} x - 9tgx - 1 0 = 0 \\ \\ tgx = t \\ \\ {t}^{2} - 9t - 1 0 = 0 \\ d = 81 + 40 = 121 \\ t1 = \frac{9 + 11}{2} = 10 \\ t2 = - 1 \\ \\ tgx = 10 \\ x1 = arctg(10) + \pi \: n \\ \\ tgx = - 1 \\ x2 = - \frac{\pi}{4} + \pi \: n$

n принадлежит Z.