[latex] sqrt{5+cosx} [/latex]= -√6 sinx

ОДЗ sinx≤0⇒x∈[3π/2+2πn;2π+2πn]5+cosx=6sin²x5+cosx-6+6cos²x=0cosx=a6a²+a-1=0D=1+24=25a1=(-1-5)/12=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πnx=4π/3+2πna2=(-1+5)/12=1/3⇒cosx=1/3⇒x=+-asrcos1/3+2πnx=3π/2+arccos1/3+2πn