#cos 3theta+cos 2theta=sin ((3theta)/2)+sin (theta/2)#
#=>2cos ((5theta)/2)cos (theta/2)=2sin thetacos (theta/2)#
#=>cos ((5theta)/2)cos (theta/2)-sin thetacos (theta/2)=0#
#=>cos(theta/2)(cos ((5theta)/2)-sin theta)=0#
When
#cos(theta/2)=0#
#=>theta/2=(2n+1)pi/2" where "n inZZ#
#=>theta=(2n+1)pi" where "n inZZ#
When #cos ((5theta)/2)-sin theta=0#
#=>cos ((5theta)/2)=cos(pi/2- theta)#
#=>(5theta)/2=2kpipm(pi/2- theta)" where "k in ZZ#
So #(5theta)/2=2kpi+(pi/2- theta)" where "k in ZZ#
#=>(7theta)/2=2kpi+pi/2" where "k in ZZ#
#=>theta=1/7(4k+1)pi" where "k in ZZ#
Again
#(5theta)/2=2kpi-(pi/2- theta)" where "k in ZZ#
#=>(5theta)/2=2kpi-pi/2+ theta" where "k in ZZ#
#=>(3theta)/2=(4k-1)pi/2" where "k in ZZ#
#=>theta=1/3(4k-1)pi" where "k in ZZ#
