#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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

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