If the period of cossinnxtanxn,n∈N,   is     6π,  then  n=

The period of cossinnx is πn and the period of tanxn is πn.Thus,    6π=  LCM πn,πnor      6π=πnλ1   or  n=λ16,and    6π=λ2πn    or   n=6λ2,λ1,λ2∈I+From n=6λ2,n=6,3,2,1.Clearly, for n = 6, we get the period of f(x) to be 6π