the average of sin2` ,sin4`,sin6`,.....,sin 180` is ---------------??PLS EXPLAIN!!!!!

firstly there are 90 terms in this series ; 45 from sin2 to sin90 and 45 from sin92 to sin 180

sin90 = 1 and sin 180 = 0 ; substitute these in the series

the series is now of 88 terms (+ 1)

sin 178 can be written as sin (180-2) = sin 2

similarly sin 92 till sin 178 can be written as sin 2 to sin 88.

the series now becomes sin² 2 , sin² 4 , ............. sin² 88    with 44 terms  (+ 1)

sin² 88 can be written as sin² (90 - 2) = cos² 2

similarly all other can be simplified with 22 terms being of cos (+1)

since sin² θ + cos² θ = 1

therefore the series will reduce to 22 ones (+1)

=23/90