5 sin^2x + 4sin ( П/2 +х ) =4

Question

5 sin^2x + 4sin ( П/2 +х ) =4

Answer 1

5sin²x+4sin(π/2+x)=4
5sin²x+4cosx=4
5(1-cos²x)+4cosx=4
5-5cos²x+4cosx-4=0
1-5cos²x+4cosx=0
5cos²x-4cosx-1=0
D=4²+1·5·4=16+20=36
cosx=(4±√36)/10
cosx=1 или cosx=-1/5
x1=2πn, n∈Z
x2=π-arccos0,2+2πn
x3=arccos0,2-π+2πn

Comments

спасибо большое