[(5cos²x+2sin²(x+π/4)-1]/
=0
ОДЗ πx-x²>0
x(π-x)>0
_ + _
____________________________
0 π
x∈(0;π)
5cos²x+2sin²(x+π/4)-1=0
5(1+cos2x)/2 +2(1-cos(2x+π/2)/2 -1=0
5+5cos2x+2+2sin2x-2=0
5+5cos2x+2sin2x=0
5cos²x+5sin²x+5cos²x-5sin²x+4sinxcosx=0
10cos²x+4sinxcosx=0 /cos²x≠0
4tgx+10=0
tgx=-2,5
x=-arctg2,5+πn