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

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

Grade:9

1 Answers

sanatan sharma
26 Points
9 years ago

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 

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