Value of tan 2 </msup> &#x2061;<!-- ⁡ --> ( 5 ) + tan

Gauge Terrell 2022-07-07 Answered
Value of tan 2 ( 5 ) + tan 2 ( 10 ) + tan 2 ( 15 ) + . . . + tan 2 ( 85 )
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Answers (1)

behk0
Answered 2022-07-08 Author has 14 answers
tan 2 ( 5 ) + tan 2 ( 10 ) + . . . + tan 2 ( 85 ) = tan 2 ( 5 π 180 ) + tan 2 ( 10 π 180 ) + . . . + tan 2 ( 85 π 180 )
= r = 1 17 tan 2 ( r π 2 18 )
Now note this result: Prove that k = 1 n 1 tan 2 k π 2 n = ( n 1 ) ( 2 n 1 ) 3
We have n=18 so then we get:
S = ( 18 1 ) ( 2 18 1 ) 3 = 595 3

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