cosx+sinx=cos2x+sin2x.
:. cosx-cos2x=sin2x-sinx.
:. -2sin((x+2x)/2)sin((x-2x)/2)=2cos((2x+x)/2)sin((2x-x)/2).
:. +sin(3/2x)sin(+1/2x)=cos(3/2x)sin(1/2x).
:. sin(3/2x)sin(1/2x)-cos(3/2x)sin(1/2x)=0.
:. sin(1/2x)[sin(3/2x)-cos(3/2x)]=0.
:. sin(1/2x)=0, or, sin(3/2x)=cos(3/2x).
Case 1 : sin(1/2x)=0.
sin(1/2x)=0 rArr 1/2x=kpi rArr x=2kpi, k in ZZ.
Case 2 : sin(3/2x)=cos(3/2x).
Note that cos(3/2x)" can not be "0, because, in that case, by the
virtue of the eqn., sin(3/2x)" will also be "0, contradicting,
sin^2(3/2x)+cos^2(3/2x)=1.
So, dividing by cos(3/2x)ne0, we get,
tan(3/2x)=1=tan(pi/4)," giving, "
3/2x=kpi+pi/4 rArr x=2/3kpi+pi/6=(4k+1)pi/6, k in ZZ.
Altogether, The Soln. Set ={2kpi}uu{(4k+1)pi/6}, k in ZZ.