2sin^2 x + 3cos x = 0 tg^2 x - tg x + 1= 0

Question

2sin^2 x + 3cos x = 0 tg^2 x - tg x + 1= 0

Answer 1

2sin^2 x + 3cos x = 0

2(1-cos^2a)+3cosx=0

2cos^2x-3cosx-2=0

D=9+16=25

cosx=3+5/4=2 нет решений т.к.  cosx e[-1,1]

cosx=-1/2    x=+-5pi/6+2pi n, neZ

 

 tg^2 x - tg x + 1= 0  

D=1-4=-3<0 нет решений</span>

Answer 2

2sin^2x+3cosx=0

2(1-cos^2x)+3cosx=0

2-2cos^2x-3cosx=0

2cos^2x-3cosx-2=0

cosx=a

2a^2-3a-2=0

d=9+16=25=5^2

a=1    a=-1/2

cosx=1

x=2Pik

cosx=-1/2

x=+-Pi/3+Pik; k ∈z