6sin^2x+5sin(p/2-x)=0 [-5p; -7p/2]

Question

6sin^2x+5sin(p/2-x)=0 [-5p; -7p/2]

Answer 1

6(1-cos²x)+5cosx=0
6cos²x-5cosx-6=0
cosx=a
6a²-5a-6=0
D=25+144=169
a1=(5-13)/12=-2/3
cosx=-2/3
x=π-arccos2/3+2πn,n∈z
x=-4π+arccos2/3∈[-5π;-7π/2]
a2=(5+13)/12=3/2⇒cosx=1,5>1 нет решения