Question

Нужно решить тригонометрические уровнения (кроме первого)

Answer 1

2)
$2 (\sin(x))^{2} + 3 \cos(x) = 0$
$2(1 - { (\cos(x)) }^{2} ) + 3 \cos(x) = 0$
$- 2( \cos(x) )^{2} + 3 \cos(x) + 2 = 0$
$2( { \cos(x)) }^{2} - 3 \cos(x) - 2 = 0$
Пусть cosx = t
$2 {t}^{2} - 3t - 2 = 0$
D = 9 - 4*2*(-2) = 25
t1 = (3+5)/4 = 2
t2 = (3-5)/4 = -1/2
cosx = 2
x= +- arccos2 + 2*pi*n, n€Z
cosx = -1/2
x = +- (pi - arccos1/2) + 2*pi*n, n€Z

3) ctgx + 3tgx = 2 sqrt (3)
1/tgx + tgx = 2sqrt (3)
(tg^2x + 1)/tgx = 2sqrt (3)
tg^x - 2sqrt (3)*tgx +1 =0
Пусть tgx=t
t^2-2sqrt (3)t+1 =0
D = 12 - 4*1 = 8
t1,2 = (2sqrt (3)+-2sqrt (2))/2
x = arctg(sqrt (3)+sqrt (2)) + pi*n, n €Z
x= arctg (sqrt (3)-sqrt (2)) + pi*n, n €Z

4) tgx = ctgx
tgx/ctgx = 1
tg^2x = 1

tgx=1
tgx=-1

x=pi/4 + pi*n, n €Z
x= -pi/4 + pi*n, n €Z

5 и 6 не уверен, как решать.