Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
1)Why is it that
sigma [ k=1 to (n-1) ] cos [2k(pi)/n] = -1 ????
2) Could you suggest any approach for this one ?
let n be an odd integer. If
sin [n(theta)] = sigma [ r=0 to n ] b (subscript r ) [sin (theta)]^r
then find the value of "b subscript 0 " and "b subsript 1 "
hi,
consider the eq.
x n -1 = 0
this eq. will have n roots, which will be the n th roots of unity,
x n = 1
x n = e i2¶k
x = e i2¶k/n
where k goes from 0 to n-1
x= 1, e i2¶/n ,e i4¶/n ,e i6¶/n .............................e i2 (n-1)¶/n
from the analysis of eq . we can tell that sum of all the roots will be 0 ,becoz the coeff. of x^(n-10 is zero here
so,
1+e i2¶/n +e i4¶/n +e i6¶/n ............................+.e i2 (n-1)¶/n =0
e i2¶/n +e i4¶/n +e i6¶/n ............................+.e i2 (n-1)¶/n = -1 hence proved
(ii)
sin nØ = b0 + b1 sinØ + b2 sin2Ø + b3 sin3Ø.................................+ bn sin nØ
in this case , we can find the values of b0 ,b1, b2.......... by succesive differentiation of both the
sides & then putting Ø =0 , in that eq.
for b0,
put Ø = 0 , we get
b0 =0
for b1,
on diff. both the sides & then putting Ø = 0, we get
b1 = n
for furthur coeff. we have to do furthur diff.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !