Question

Решите уравнение. 1/cos^2 х +3 tgx - 5 =0

Answer 1

1/cos^2 х +3 tgx - 5 =0

1 + tg^2 x + 3 tgx - 5 =0

tg^2 + 3tgx - 4 =0

 

Пусть tgx=t, тогда

t^2 + 3t - 4=0

t1+t2 = -3

t1*t2 = -4

 

t1 = 1

t2 = -4

 

tgx = 1

x = pi/4

 

tgx = -4

x = - arctg4