CBSE Class 11-science Answered
Find ∑_(r=0)^7〖tan〗^2 πr/16
(STATEMENT : the sum of r varies from 0 to 7 for t tan^2 pi r/16)
Give answer in proper steps.
Asked by acv27joy | 18 May, 2018, 05:47: PM
Expert Answer
7∏/16 = ∏/2 - ∏/16
6∏/16 = ∏/2 - 2∏/16
5∏/16 = ∏/2 - 3∏/16
4∏/16 = ∏/4
tan2 0 + tan2 ∏/16 + tan2 2∏/16 + tan2 3∏/16 + tan2 4∏/16 + tan2 5∏/16 + tan2 6∏/16 + tan2 7∏/16
0 + tan2 ∏/16 + tan2 2∏/16 + tan2 3∏/16 + tan2 ∏/4 + tan2 (∏/2 - 3∏/16) + tan2 (∏/2 - 2∏/16) + tan2 (∏/2 - ∏/16)
tan2 ∏/16 + tan2 2∏/16 + tan2 3∏/16 + 1 + cot2 3∏/16 + cot2 2∏/16 + cot2 ∏/16
tan2 ∏/16 + cot2 ∏/16 + tan2 2∏/16 + cot2 2∏/16 + tan2 3∏/16 + 1 + cot2 3∏/16 + 1
Solving these brackets you will get the answer.
[tan2 ∏/16 + cot2 ∏/16] = (tan ∏/16 + cot ∏/16)2 - 2 tan ∏/16 cot ∏/16
Solving this we get 8√2 (√2 + 1) - 2
Solve remaining bracket.
Answered by Sneha shidid | 21 May, 2018, 12:05: PM
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