The greatest value of the term independent (Coefficient of x0) of x in the expansion of xSinα+Cosαx8,α∈R is

Tr+1=8Cr(xSin⁡α)8−rCos⁡αxr=8Crx8−2rSin8−r⁡αCosr⁡α Independent term means 8−2r=0⇒8=2r⇒r=4∴T4+1=8C4Sin4⁡αCos4⁡α=8c424Sin4⁡(2α) Greatest value =8c424∵ Greatest value of Sin4⁡(2α)=1 )