Question

If 13α=π,show that, cos3α+cos5α+2cosαcos9α=0

Answer 1

cos3a+cos5a+cos(a+9a)+cos(9a-a)= 0
=cos3a+cos5a+cos10a+cos8a
=(cos10a+cos3a)+(cos8a+cos5a)
=2cos(13a/2)cos(7a/2)+ 2cos(13a/2)cos(3a/2)
=2cosπ/2cos(7a/2)+2cos(π/2)cos3(3a/2)
=0
since,cos(π/2)=0